JlOLOft 


A  TEXT-BOOK   OF  ELECTRO-CHEMISTRY 


A  TEXT-BOOK  OF 
ELECTRO-CHEMISTRY 


BY 


MAX  LE  BLANC 
u 

PROFESSOR    IN   THE   UNIVERSITY   OF   LEIPZIG 


TRANSLATED  FROM  THE  FOURTH  ENLARGED  GERMAN 
EDITION 

BY 

WILLIS  E.   WHITNEY,  Pn.D. 

DIRECTOR   OF   THE    RESEARCH   LABORATORY   OF   TOT 
GENERAL   ELECTRIC    COMPANY 

AND 

JOHN  W.   BEOWN,  PH.D. 

DIRECTOR   OF   THE    RESEARCH   AND   BATTERY    LABORATORY 
OF   THE   NATIONAL   CARBON   COMPANY 


THE    MACMILLAN    COMPANY 

LONDON:  THE  MACMILLAN  CO.,  LTD. 
1918 

All  rights  reserved 


Vqo7 


1       ^-^J^.        5/ 

COPYRIGHT,  lio7, 
BY  THE  MACMILLAN  COMPANY. 

Set  up  and  electrotyped.    Published  March,  1907.     Reprinted 
March,  1910  ;  January,  1913;  July,  1916;  September,  1917. 


NorurooU 
J.  8.  Gushing  Co.  —Berwick  &  Smith  Co. 

Norwood,  Mass.,  U.S.A. 


HIS  TEACHER 
PROFESSOR  WILHELM  OSTWALB 

THIS   BOOK 

IS  GRATEFULLY  DEDICATED 
BY  THE  AUTHOR 


417680 


EXTRACT  FROM  THE  AUTHOR'S  PREFACE  TO 
THE   FIRST  EDITION 

THE  present  work  was  nearly  completed  in  connection  with  the 
course  of  lectures  given  by  me  during  the  winter  of  1894-1895.  It 
is  meant,  first  of  all,  for  students  of  science;  for  such  persons  as, 
having  completed  their  studies,  are  already  in  practice;  and,  finally, 
for  whoever  is  interested  in  electro-chemistry.  I  have  endeavored 
to  write  as  clearly  and  simply  as  possible,  but  those  who  have  but 
slight  previous  knowledge  must  study  the  book  carefully  in  order 
to  obtain  the  greatest  benefit  from  it.  In  modern  electro-chemistry 
there  are  certain  methods  of  conception  which  any  one  studying  the 
subject  must  make  his  own,  and  this  cannot  be  done  without  work. 

M.   LE  BLANC. 

LEIPZIG,  September,  1895. 


rii 


AUTHOR'S    PREFACE   TO   THE    FOURTH    EDITION 

DURING  the  three  years  which  have  passed  since  the  appearance 
of  the  third  edition  of  this  book,  an  abundance  of  work  has  appeared 
in  the  domain  of  electro-chemistry.  The  difficulty  of  including 
all  of  the  essentials  of  the  science  without  unduly  increasing  the 
size  of  the  book  is  continually  increasing.  I  have  given  my  best 
effort  to  overcome  it. 

Up  to  the  present  there  has  appeared  an  English  translation  of 
the  first  edition,  an  Italian  translation  of  the  second  edition,  and 
a  French  translation  of  the  third  edition  of  this  book. 

Shortly  after  the  appearance  of  this,  the  fourth  German  edition, 
an  English  translation  of  it  will  be  published. 

For  assistance  in  reading  the  proofs,  I  am  this  time  indebted  to 
G.  Just,  Ph.D.,  and  A.  Konig,  Dipl.  Ing.  I  am  also  indebted  to 
Professor  Abegg  for  valuable  suggestions. 

M.   LE  BLANC. 

KARLSRUHE,  BADEN, 
August,  1906. 


viii 


TRANSLATORS'   PREFACE 

THE  present  work  is  a  translation  of  the  fourth  German  edition, 
and  is  essentially  a  revision  and  enlargement  of  that  of  the  first 
German  edition  prepared  by  one  of  the  present  translators.  Although 
in  its  preparation  the  earlier  translation  has  been  freely  used,  the 
changes  and  additions  made  by  Professor  Le  Blanc,  as  well  as 
minor  additions  introduced  by  the  present  translators,  have  either 
necessitated  or  rendered  advisable  the  rewriting  of  a  large  part  of 
the  book.  The  additions  made  by  the  translators  have  been  in- 
closed in  brackets. 

Special  attention  has  been  given  to  the  following:  — 

The  Notation.  A  consistent  system  of  notation  has  been  used 
throughout  the  book.  An  outline  of  it  will  be  found  in  the  Appendix. 

TJie  Nomenclature.  We  have  endeavored  to  make  the  nomen- 
clature conform  to  that  of  the  best  recent  text-books  of  electricity 
and  chemistry. 

TJie  Illustrations.  Of  the  52  illustrations,  25  are  new  ones  intro- 
duced by  the  translators,  and  21  have  been  redrawn. 

Special  credit  is  due  Mrs.  J.  W.  Brown  for  aid  in  preparing  the 
manuscript  and  in  reading  the  proofs. 

W.  R.  WHITNEY, 
J.  W.  BKOWN. 


CONTENTS 


CHAPTER  I 

THE    FORMS    OF    ENERGY   AND    THEIR  MEASUREMENT. 

THE       FUNDAMENTAL      PRINCIPLES  RELATING      TO 
ELECTRICAL     ENERGY 

PAOB 

Energy  and  its  forms    .        .        ,        .        ...  •        *        .        .        1 

Measurement  of  mechanical,  heat,  and  electrical  energy  .        .        .        .        1 

Electric  currents  and  their  properties  .        ...  .        .        ...        5 

Electromotive  force,  current,  and  resistance        .        .  ...        .        7 

Electrical  equivalent  of  heat         .        .        .        .        .  .        y       ••        .15 

Electric  furnace  and  its  industrial  importance     .        .  .        .        .*               18 

Dark  or  silent  electrical  discharge        .        .        .        .  .        »        ...      23 

Electrical  capacity     '..' .        •        »        .      24 

Positive  and  negative  electricity.    The  electrometer    .  .        .        .        .      25 

Electrical  measurements 27 


CHAPTER  II 

DEVELOPMENT  OF  ELECTRO-CHEMISTRY  UP  TO 
THE  PRESENT   TIME 

Earliest  records  of  electrical  phenomena      .        .        .        ...       .  31 

Work  of  Galvani  ....        .        .        .        .        '.        .        .        .  32 

Work  of  Volta.     The  Voltaic  pile        ......        .        .        .33 

Electrolytic  decomposition  of  water      .        .      ".        .        .  •,     .        .        .  36 

Measurements  of  the  potentials  of  a  Voltaic  pile          .        .        ....  37 

Migration  of  acid  and  alkali  and  the  discovery  of  the  alkali  metals     .        .  38 

Rise  and  fall  of  the  electro-chemical  theory  of  Berzelius      .        .  40 

Laws  of  electro-chemical  change  .        ...        .        *        .        .        .  42 

Electro-chemical  nomenclature     .........  44 

Development  of  the  present  theory  of  electrolysis.     The  Grotthus  theory  .  44 

Conductance  of  solutions  and  the  constitution  of  ions          ....  45 

Replacement  of  the  Grotthus  theory  by  the  Clausius  theory         ...  47 

Relation  between  chemical  and  electrical  energy  I 49 

xi 


xii  CONTENTS 


CHAPTER   III 
THE  THEORY   OP  ELECTROLYTIC  DISSOCIATION 

PAGE 

The  laws  and  theories  relating  to  osmotic  pressure 52 

Abnormality  of  acids,  bases,  and  salts.     Electrolytic  dissociation       .        .  57 

Calculation  of  the  degree  of  dissociation 58 

Dissimilarity  between  gaseous  and  electrolytic  dissociation.    The  ions       .  59 

lonization  according  to  the  material  conception  of  electricity      ...  60 


CHAPTER   IV 
THE  MIGRATION   OF  IONS 


The  migration  of  ions 


CHAPTER  V 

THE  CONDUCTANCE  OF  ELECTROLYTES 

Specific  and  equivalent  conductance 85 

General  regularities      .        .        .        .        ...        .        .        .        .        .89 

Application  of  the  mass-action  law  to  gaseous  and  to  electrolytic  disso- 
ciation  .............  95 

Determination  of  the  electrical  conductance  of  electrolytes.     The  method 

of  Kohlrausch 98 

Method  of  Nernst  and  Haagn 104 

Calculation  of  the  dissociation  constant  from  electrical  conductance    .        .  105 
Relation  between  dissociation  constants  and  chemical  constitution     .        .111 
Velocity  of  migration  of  individual  ions       .        ...,        .        .116 

The  absolute  velocities  of  the  ions        .      •  '.'".        .        .        .        .        .  119 

Electrolytic  frictional  resistance   .........  123 

The  limited  applicability  of  the  Ostwald  dilution  law.     Empirical  rules      .  124 

The  conductivity  and  degree  of  dissociation  of  water  .....  128 

Supersaturated  solutions      ..........  129 

Temperature  coefficient 130 

Heat  of  dissociation 133 

Influence  of  pressure 135 

Mixed  solutions.   Isohydric  solutions.    Application  of  electrical  conductivity 

to  chemical  analysis 136 

Regularity  of  ionization.     Reactivity  of  electrolytes    .....  141 
Solvents  other  than  water.     Relation  between  the  dissociating  power  and 

the  dielectric  constant  of  solvents          .                 142 

The  internal  friction  and  conductance  of  organic  solvents    .        .        .        .151 

The  electrical  conductance  of  salts  in  the  fused  and  solid  states  .        .        .  163 


CONTENTS  xiii 


Unipolar  conduction .154 

Technical  importance  of  electrical  conductivity 155 


CHAPTER  VI 

ELECTRICAL  ENDOSMOSE.  MIGRATION  OP  SUSPENDED 
PARTICLES  AND  OP  COLLOIDS.  ELECTRO-STENOLY- 
SIS 

Electrical  endosmose.     Migration  of  suspended  particles  and  of  colloids. 

Electro-stenolysis 157 

CHAPTER  VII 

ELECTROMOTIVE  FORCE 

The  determination  of  electromotive  force 161 

Reversible  and  irreversible  cells 164 

Relation  between  chemical  and  electrical' energy  II 165 

Electrolytic  solution  pressure       .........  175 

Calculation  of  the  electromotive  force  existing  at  the  surface  of  reversible 

electrodes       ............  181 

Concentration  cells       .        .        .        .        .        .        .        .        .        .        .184 

Different  concentration  of   the  substances  which  are  electromotively 

active 184 

Different  concentrations  of  the  ions          .......  197 

Concentration  double-cells         .        .        .  .        .        .        .        .211 

Use  of  the  electrometer  as  an  indicator  in  titration 216 

Liquid  cells 217 

General  consideration  of  concentration  and  liquid  cells        ....  224 

Thermoelectric  cells  —  the  electromotive  series 228 

Chemical  cells 231 

Determination  of  single  potential-differences 234 

Influence  of  negative  ions  upon  the  potential-difference,  Metal  —  metal 

salt  solution   .        ...        ... 249 

Cells  in  which  the  electromotively  active  substances  are  not  elements          .  250 
Formation  of  potential-difference  at  the  electrodes.     Spontaneous  evolution 

of  oxygen  or  hydrogen.     The  process  of  current  production          .        .  263 

Electromotive  force  and  chemical  equilibrium 267 

Velocity  of  ionization.     Passivity.     Catalytic  influence       ....  275 

General  theory  of  the  course  of  the  electro-chemical  reactions     .        .        .  281 

Elements  possessing  double  natures 284 


xiv  CONTENTS 

CHAPTEE   VIII 
ELECTROLYSIS   AND   POLARIZATION 

PA6R 

Method  of  measuring  polarization 286 

Decomposition  values  of  the  electromotive  force.     The  hydrogen-oxygen 

cell.     Primary  and  secondary  decomposition  of  water          .        .        .  288 
Importance  of  the  decomposition  voltage  in  making  electrolytic  separations 

and  in  preparing  new  compounds .        .        .  •     . '       .        .        .        .  309 

Electrolysis  with  an  alternating  current   .......  316 

Electrolysis  without  electrodes        ' .        .        <        .        .        .        .        .  317 

Decomposition  voltage  and  solubility        ...        .        .        .        .        .318 

CHAPTEE   IX 

SUPPLEMENT.     STORAGE  CELLS  OR  ACCUMULATORS 

Supplement.    Storage  cells  or  accumulators 321 

APPENDIX 

NOTATION 

Notation  .  .  .    327 


A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 


A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 


CHAPTER   I 

THE  FORMS  OF  ENERGY  AND  THEIR  MEASUREMENT. 
THE  FUNDAMENTAL  PRINCIPLES  RELATING  TO  ELEC- 
TRICAL ENERGY 

Energy  and  its  Forms. — A  clear  conception  of  the  funda- 
mental principles  relating  to  the  forms  of  energy,  especially  of 
electrical  energy,  is  essential  to  the  successful  study  of  electro- 
chemistry. For  this  reason,  before  beginning  the  study  of  electro- 
chemistry proper,  these  principles  will  be  considered  briefly. 

Energy  plays  a  most  important  part  in  human  affairs.  When 
food  or  coal  is  bought,  it  is  the  energy  content  that  chiefly  concerns 
the  buyer.  Similarly  when  a  current  of  electricity  is  delivered  to 
the  consumer,  it  is  the  quantity  of  electrical  energy  so  delivered 
that  is  of  greatest  importance  and  that  determines  the  price  to 
be  paid. 

Energy  may  be  subdivided  into  five  distinct  kinds  or  forms  of 
energy;  namely:  — 

MECHANICAL  ENERGY, 

HEAT  ENERGY, 

ELECTRICAL  ENERGY, 

CHEMICAL  ENERGY,  AND 

RADIANT  ENERGY. 

These  forms  of  energy  are  mutually  transmutable. 

The  Measurement  of  Mechanical,  Heat,  and  Electrical  Energy. 
—  The  units  used  in  the  measurement  of  mechanical  energy  are 
grouped  into  two  systems;  namely,  the  Meter-Kilogram-Hour 
(M.  K.  H.)  System  and  the  Centimeter-Gram-Second  (C.  G.  S.)  Sys- 
tem. In  the  former,  the  technical,  system,  the  unit  of  mechanical 
energy  or  work  is  that  quantity  of  energy  or  work  which  is  required  to 
raise  a  kilogram  weight  one  meter  in  height.  In  the  centimeter-gram- 
B  1 


2  A   TEXT -BOOK  OF  ELECTRO-CHEMISTRY 

second  system,  which  is  used  in  all  exact  scientific  work,  the  unit  of 
mechanical  energy,  the  erg,  is  that  quantity  of  energy  or  work  which 
is  required  to  displace  a  unit  of  force  through  a  unit  distance.  The 
unit  of  force,  the  dyne,  is  defined  to  be  that  force  which  is  required 
to  produce  an  acceleration  of  one  centimeter  per  second  in  a  mass  of 
one  gram.  The  relations  between  these  units  are  represented  by  the 
following  equations :  — 

Force  (F)  in  dynes  =  Mass  (M )  in  grams  x  Acceleration  (A)  in 
centimeters  per  second. 

Mechanical  energy  (Em)  in  ergs  =  Work  ("FT)  in  ergs  =  Force  (F) 
in  dynes  x  Distance  (d)  in  centimeters. 

In  scientific  work,  it  is  very  important  to  distinguish  clearly 
between  mass  and  weight.  Mass  is  an  unchangeable  property  of 
matter,  while  weight,  since  it  is  the  force  with  which  a  quantity  of 
matter  is  drawn  toward  the  earth's  center,  is  a  property  of  matter 
which  varies  according  to  the  location  on  the  earth's  surface.  The 
unit  of  mass,  called  the  gram-mass,  is  defined  to  be  equal  to  the 
mass  of  one  cubic  centimeter  of  water  at  four  degrees,1  the  tempera- 
ture of  its  maximum  density.  That  mass  of  any  other  substance 
which,  under  the  influence  of  a  given  force,  receives  the  same  accel- 
eration as  does  one  cubic  centimeter  of  water,  under  the  influence  of 
the  same  force,  may  also  be  taken  as  a  unit  of  mass.  The  unit  of 
weight,  called  the  gram-weight,  is  defined  to  be  that  force  with  which 
a  gram-mass  is  attracted  toward  the  earth's  center.  Since  this 
attractive  force,  at  a  latitude  of  45  degrees  and  at  sea  level,  pro- 
duces an  acceleration  of  980.6  centimeters  per  second  in  a  gram-mass 
when  falling  freely,  it  is  equal  to  980.6  dynes. 

The  relations  which  exist  between  the  technical  unit,  the  meter- 
kilogram,  and  the  scientific  units,  the  gram-centimeter,  the  erg,  and 
the  joule,  are  given  by  the  following  equations :  — 

1  M.  Kgm.  =  105  cm.  gm.  =  105  x  980.6  ergs  =  9.806  joules. 

With  these  units  defined,  it  is  now  possible  to  measure  and  to 
compare  various  quantities  of  mechanical  energy,  or  work. 

The  unit  of  heat  energy,  called  the  calorie,  is  that  quantity  of  heat 
which  is  required  to  raise  one  gram  of  water  from  15°  to  16°  t. 

Having  now  defined  the  units  for  two  of  the  energy  forms,  it  is 
possible,  with  the  aid  of  the  law  of  the  conservation  of  energy,  to 
determine  the  relation  between  these  units.  By  direct  experiment,  a. 

1  As  a  matter  of  fact,  however,  the  unit  of  mass  is  one  thousandth  part  of  the 
mass  of  a  certain  piece  of  platinum  kept  at  Paris,  which  is  very  nearly  one  thousand 
times  as  great  as  the  above  theoretical  unit. 


FORMS  OF  ENERGY  AND  THEIR  MEASUREMENT 


3 


known  quantity  of  mechanical  energy  has  been  completely  trans- 
formed into  heat  energy,  showing  the  following  relation  between  the 
units  of  mechanical  and  those  of  heat  energy :  — 

.1890  x  107  ergs  or  42720  cm.  gms.  =  1  calorie. 

This  relation  between  the  erg  or  joule  and  the  calorie  is  called  the 
mechanical  equivalent  of  heat. 

In  an  analogous  manner,  the  relations  between  the  units  of  all  the 
other  forms  of  energy  could  be  found  if  units  for  these  forms  of  energy 
were  known.  Since,  however,  besides  mechanical  and  heat  energy, 
only  electrical  energy  has,  at  present,  well-defined  units,  there 
remains  to  be  considered  an  electrical-heat,  and  an  electrical- 
mechanical,  equivalent. 

Accepting  the  transmutability  of  the  energy  forms  without  ques- 
tioning the  conditions  under  which  such  transmutation  takes  place, 
the  case  of  transference  of  energy  between  two  systems  in  contact 
with  each  other  and  containing  unequal  quantities  of  the  same 
form  of  energy  will  now  be  studied.  This  study  will  be  carried  out 
with  two  gaseous  systems  possessing  different  quantities  of  volume 
energy,  a  kind  of  mechanical  energy  which  may  be  expressed  in 
terms  of  the  mechanical  units  already  defined. 

Let  us  first  consider  the  system  represented  by  Figure  1,  consist- 
ing of  a  gas  reservoir  Q  closed  by  a  weightless  and  f rictionless  pis- 
ton p,  and  placed  in  the  vacuum  V. 
The  gas  contained  in  the  reservoir 
is  now  said  to  possess  a  definite  vol- 
ume energy,  since  it  possesses  the 
power  of  doing  a  definite  quantity 
of  work  by  expanding  against  a 
pressure.  If,  when  the  gas  sup- 
ports a  100-gram  weight  upon  the 
piston,  the  latter  is  in  the  position 
a,  and  if,  upon  heating  the  gas, 
the  piston  and  weight  are  raised  to 
the  position  6,  50  centimeters  above  FIG.  l 

a,  a  weight  of  100  grams  is  raised 

50  centimeters  at  the  expense  of  the  volume  energy  of  the  gas. 
The  work  done  may  be  expressed  as  follows :  — 

W=  JF(100  gms.)  x  d  (50  cms.)  =  5000  gm.  cms. 
If,  now,  the  piston  has  a  cross  section  of  100  square  centimeters, 


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Gas  9. 

4  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

each,  square  centimeter  of  it  exerts  a  pressure  of  one  gram  on  the  gas. 
The  gas  is,  then,  under  a  pressure  of  one  gram  per  square  centi- 
meter. The  volume  increase,  when  the  piston  rises  from  a  to  b, 
is  5000  cubic  centimeters.  Hence  the  product  of  the  pressure,  in 
grams  per  square  centimeter,  and  the  volume,  in  cubic  centimeters, 
is  5000,  a  value  identical  with  the  number  of  gram-centimeters  of 
work  done  during  the  expansion.  The  work  done  may  therefore  be 
expressed  as  follows :  — 

Work  =  Pressure  (1  gin.)  x  Volume  (5000  cu.  cm.)  =  5000  gm.  cm. 

Let  us  next  consider  the  horizontal  vessel  represented  in  Figure  2, 
which  is  provided  with  a  movable  piston  p,  on  one  side  of  which  is 

hydrogen  and  on  the  other 
nitrogen.  If,  now,  the 
two  gases  exert  equal 


hqdrogei? 


po/14 


pressure  upon  the  piston, 
it  remains  motionless  and 
no  transference  of  energy 
from  one  gas  to  the  other 

takes  place,  although  the 
FIG.  2  ,    ,         , 

energy  possessed   by  the 

nitrogen  is  much  greater  than  that  possessed  by  the  hydrogen. 
This  difference  in  the  energy  of  the  two  gases  can  be  made  as  great 
as  desired  by  increasing  the  volume  of  the  nitrogen  and  decreasing 
that  of  the  hydrogen,  without  causing  the  piston  to  move.  Hence 
it  is  evident  that  the  quantity  of  energy  possessed  by  the  two  gases 
does  not  determine  whether  or  not  a  transference  of  energy  will 
take  place  between  them.  If,  however,  we  decrease  the  volume,  and 
thus  increase  the  density  and  consequently  the  pressure  of  one  of 
the  gases,  the  piston  is  at  once  set  in  motion,  resulting  in  an  expan- 
sion of  the  gas  under  the  greatest  pressure  and  a  corresponding  com- 
pression of  the  other.  During  this  change,  the  gas  undergoing 
expansion  loses  a  definite  quantity  of  volume  energy,  while  that 
undergoing  compression  gains  the  same  quantity.  When  the  piston 
has  again  come  to  rest,  the  same  pressure  is  exerted  upon  the 
piston,  by  each  of  the  two  gases.  The  relative  pressures,  then,  and 
not  the  relative  volumes  of  the  two  gases,  determine  whether  or  not  a 
transference  of  energy  will  take  place  between  the  two  gases. 

It  has  already  been  shown  that  the  volume  energy  of  a  gas  may 
be '  represented  as  the  product  of  two  factors  according  to  the 
equation, 

Ev=pv. 


FORMS  OF  ENERGY   AND   THEIR  MEASUREMENT  5 

The  factor  p,  as  shown  above,  determines  the  equilibrium  of  a 
gaseous  system  and  for  this  reason  is  called  the  intensity  factor.  The 
other  factor  v  is  denned  by  the  equation, 

_  Ev  _  Volume  Energy 
"  p  ~  Intensity  Factor' 

It  determines  the  quantity  of  volume  energy  for  any  given  value 
of  the  intensity  factor  p,  and  is  called  the  capacity  factor. 

A  similar  resolution  of  several  of  the  other  forms  of  energy  into 
two  such  factors  has  been  made,  which  has  greatly  facilitated  the 
understanding  of  energy  phenomena.  In  each  case,  the  following 
general  equations  represent  the  relation  between  the  energy  E,  its 
intensity  factor  f{  and  its  capacity  or  quantity  factor  fc. 


The  intensity  and  capacity  factors  of  electrical  energy  Ee  are 
the  electromotive  force  F  and  the  quantity  of  electricity  Q.  The 
relation  between  electrical  energy  and  its  factor  is,  then,  represented 
by  the  equation, 

Ee  =  F  X  Q. 

This  will  be  made  clearer  in  the  following  pages. 

Electric  Currents  and  their   Properties.  —  On    account    of    our 
limited   sense  of  perception   of   electrical   phenomena,  we   cannot 
comprehend    them    to    the    extent   possible    in   the  case   of    the 
phenomena    of    mechanical    en- 
ergy.    In  order  to  comprehend  — ^v 
and  control  them  the  actions  and 
effects  of  electrical  energy  must 
be  studied,  for  even  the  idea  of 
a  unit  of  work  or  of  a  unit  of 
length,  such  as  the  meter,  could 
not  be  comprehended  if  the  ac- 
tion of  a  unit  of   work  or  the 
length  represented  by  the  meter 
had  not  been  observed. 

Consider  a  vessel  divided  into 
two  parts  by  means  of  a  porous 

plate,  e.  g.,  of  unglazed  porcelain,  as  shown  in  Figure  3.  If 
into  one  part  of  the  vessel  is  poured  a  solution  of  copper  sulfate, 
and  into  the  other  a  solution  of  zinc  sulfate,  and  a  rod  of  copper  is 
placed  in  the  copper  sulfate  solution  and  a  rod  of  zinc  in  the  zinc 


CaSQ, 


FIG.  3 


6  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

sulfate  solution,  we  have  an  arrangement  called  a  galvanic  cell.  If 
now  the  zinc  and  copper  rods,  the  two  poles  of  the  cell,  be  connected 
by  means  of  a  wire,  the  latter  becomes  heated.  If  a  magnetic  needle 
be  placed  near  the  wire,  the  needle  is  turned  from,  its  natural 
position.  Finally,  if  the  wire  be  cut,  its  two  ends  fastened  to 
pieces  of  platinum  foil,  and  these  pieces  of  foil  be  dipped  into  a 
solution  of  copper  sulfate  in  such  a  manner  that  they  are  not  in 
contact  with  each  other,  it  is  observed  that  metallic  copper  deposits 
upon  one  of  the  pieces  of  platinum. 

From  these  observations,  we  must  conclude  that  something  has 
taken  place  in  the  wire,  for  the  wire  always  produces  these  three 
effects  when  connecting  the  zinc  and  copper  poles  of  the  cell  and 
never  produces  them  when  disconnected  from  them.  Whenever  a 
wire  produces  these  effects,  a  current  of  electricity  is  said  to  be  passing 
or  flowing  through  it. 

It  is  conceivable  that  a  wire  might  be  found  which,  when  con- 
necting the  poles  of  a  galvanic  cell,  would  affect  the  magnetic 
needle  but  not  become  heated,  which,  therefore,  would  not  produce  all 
of  the  three  effects  stated  above  to  be  characteristic  of  a  wire  conduct- 
ing an  electric  current.  This  was  formerly  supposed  by  many  to  be 
true,  but,  as  a  matter  of  fact,  such  is  not  the  case.  From  long 
experience,  it  is  known  that  whenever  a  wire  produces  one  of  these 
three  effects  it  always  produces  the  other  two,  together  with  a 
number  of  other  effects  which  are  not  of  interest  at  this  point. 
That  some  of  these  effects  may  be  made  inappreciably  small  does 
not  contradict  the  above  statement. 

These  properties  of  the  electric  current  which  serve  to  detect  its 
presence  being  known,  it  is  now  possible  by  means  of  suitable 
arrangements  to  study  the  other  properties  of  the  electric  current. 
Considering  again  the  galvanic  cell,  if  the  wire  is  left  in  its  former 
position  with  the  exception  that  the  end  which  was  joined  to  the 
zinc  rod  is  now  joined  to  the  copper  rod,  and  the  other  end  is  now 
joined  to  the  zinc  rod,  the  same  effects  of  the  electric  current  are 
again  observed  with  the  simple  difference  that  the  magnetic  needle 
is  deflected  in  the  opposite  direction,  and  that  the  metallic  copper  is 
deposited  upon  the  other  piece  of  platinum.  Therefore  we  may 
properly  speak  of  the  direction  of  an  electnc  current. 

Naturally,  the  next  thing  to  be  determined  is  whether  the  deflec- 
tion of  the  magnetic  needle  or  the  amount  of  copper  deposited  upon 
the  platinum  in  a  given  time  remains  constant  or  varies,  and,  in  the 
latter  case,  to  determine  upon  what  the  variation  depends.  If,  to 
this  end,  the  connecting  wire  be  lengthened,  it  is  observed  that  the 


FORMS  OF  ENERGY  AND  THEIR  MEASUREMENT 


7 


rate  of  the  deposition  of  copper  is  decreased ;  while  if  the  wire  is 
shortened,  the  rate  is  increased.  We  must  conclude  from  these  facts 
that  the  electric  current  has  a  strength  depending  upon  circumstances. 
This  gives  us  the  conception  of  current-strength  of  an  electric  current. 

The  current-strength  varies  inversely  as  the  length  of  the  connect- 
ing wire.  Therefore  the  wire  hinders  or  opposes  to  a  certain  extent 
the  passage  of  the  electric  current,  and  is  said  to  possess  a  certain 
resistance. 

It  has  now  been  observed  that  the  greater  the  resistance  of  the  wire, 
the  less  the  current.  The  question  now  arises  whether  or  not  it  is  pos- 
sible to  change  the  current-strength  without  changing  the  resistance. 
Experiment  has  shown 
that  it  is  possible  to  thus 
change  the  current.  If, 
instead  of  using  one  gal- 
vanic cell,  two  are  used, 
the  zinc  rod  of  one  cell 
being  connected  with  the 
copper  rod  of  the  other, 
as  shown  in  Figure  4,  it  n^Sd  ZwSO 


I 


is  observed  that  a  much 

greater    current    is    ob-  FlG  4 

tained,  although  the  re- 
sistance of  the  second  cell  has  been  added  to  that  of  the  wire ;  that 
is  to  say,  the  electric  current  starting  say  at  a  must  pass  through 
the  wire  ac  and  also  through  the  cell  II  before  it  reaches  the 
pole  b.  The  second  cell  acts  as  if  it  had  increased  the  pressure  or 
force  by  which  the  electric  current  is  driven  through  the  wire. 
Consequently,  we  come  to  speak  of  the  electrical  pressure,  or  electro- 
motive force  P  of  the  current. 

It  is  assumed  that  the  terms  current,  resistance,  and  electromotive 
force  are  no  longer  meaningless  concepts,  but  that  they  possess  a  real 
significance  to  the  reader.  We  may,  therefore,  proceed  to  the  con- 
sideration of  the  units  in  which  these  quantities  are  expressed.  This 
consideration  will  be  of  a  much  simpler  nature  than  that  by  which 
the  units  were  first  established. 

Electromotive  Force,  Current,  and  Resistance.  —  The  electromotive 
force  of  a  galvanic  cell  such  as  has  been  used  in  the  previous  discus- 
sion (called  the  Daniell  cell,  from  its  discoverer),  when  the  concen- 
tration of  the  copper  sulfate  is  equal  to  the  concentration  of  the  zinc 
sulfate,  is  defined  to  be  1.10  units,  called  volts.  The  resistance  of  a 
column  of  mercury,  106.3  centimeters  in  length  and  one  square  milli- 


8  A  TEXT-BOOK  OF   ELECTRO-CHEMISTRY 

meter  in  cross  section,  at  0°  t,  is  defined  to  be  one  unit,  called  an  ohm. 
Finally,  a  current  which  deposits  0.3294  milligram  of  copper  in  a 
second  is  defined  to  be  one  unit,  called  an  ampere.1  These  units 
may  be  tabulated,  briefly,  as  follows  :  — 

Unit  of  E.  M.  F.  =  Volt  =  E.  M.  F.  of  the  Daniell  cell  -f-  1.10. 
Unit  of  current  =  Ampere  =  Current  which  deposits  0.33  mg.  of 

copper  per  second. 

Unit  of  resistance  =  Ohm  =  Resistance  of  a  mercury  column,  106.3 
cm.  x  1  sq.  mm. 

Why  these  particular  values  have  been  chosen  as  units  need  not  be 
discussed  here,  for  this  question  belongs  more  to  the  history  of 
electrical  science. 

It  has  already  been  observed  that  the  current  depends  upon  the 
electromotive  force,  on  the  one  hand,  and  upon  the  resistance  on  the 
other.  The  assumption  was  made  by  Ohm  that  the  current  is 
directly  proportional  to  the  electromotive  force  and  inversely  pro- 
portional to  the  resistance.  This  assumption,  which  is  also  expressed 
by  the  equation, 

Current  (c)  =  ^  Electromotive  force  (F) 
Resistance  (R) 

has  been  found  by  experiment  to  be  universally  true.  In  this  equa- 
tion, K  is  a  ratio  factor,  depending  on  the  units  in  which  the  current, 
electromotive  force,  and  resistance  are  expressed.  However,  the 
units  defined  above  are  so  related  that  if,  in  a  circuit  whose  resist- 
ance is  one  ohm,  an  electromotive  force  of  one  volt  exists,  the  cur- 
rent flowing  through  the  circuit  is  one  ampere.  Consequently  the 
above  factor  in  this  case  is  equal  to  unity.  Hence  the  equation, 

Ampere  = 


Ohm 

With  the  above  units  and  their  mutual  relation  known,  it  is  now 
possible  to  consider  how  an  unknown  electromotive  force  or  an  un- 
known resistance  may  be  determined.  It  is  evident  that  the  current 
in  amperes  may  be  determined  by  simply  finding  the  number  of 
milligrams  of  copper  deposited  by  the  current  in  one  second  and 
dividing  by  the  number  of  milligrams  of  copper  deposited  in  the 

1  These  terms,  volt,  ohm,  ampere,  coulomb,  farad  (the  last  two  terms  will 
be  explained  later),  have  been  derived  from  the  names  of  the  following  pioneers 
of  electrical  science  :  Volta,  Ohm,  Ampere,  Coulomb,  and  Faraday. 


FORMS  OF  ENERGY  AND  THEIR  MEASUREMENT    9 

same  time  by  a  current  of  one  ampere,  namely,  by  0.3294.      This  is 
also  expressed  by  the  equation, 

r  N      milligrams  of  copper  deposited  per  second 

c(m  amperes)  =  •  %.329/ 

The  resistance  of  the  circuit  may  now  be  determined  by  connect- 
ing it  to  the  poles  of  a  Daniell  cell  and  measuring  the  current  pro- 
duced by  it  in  the  manner  just  outlined.  If  the  current  is  found  to 
be  0.001  ampere,  then,  since  the  electromotive  force  of  the  Daniell 
cell  is  equal  to  1.10  volts,  the  resistance  may  be  calculated  by  means 
of  Ohm's  law  as  follows  : 


*=,*. 

c 
Then,  by  substitution  of  numerical  for  literal  values, 

R=     1M  volt3     =1100  ohms. 
0.001  ampere 

Finally,  an  unknown  electromotive  force  may  be  determined  by 
introducing  it  in  the  above  circuit  in  place  of  the  Daniell  cell,  the 
resistance  of  the  circuit  remaining  unchanged,  and  again  measuring 
the  current  produced  in  the  circuit.  If,  in  this  case,  the  current  is 
found  to  be  equal  to  0.01  ampere,  then,  since  the  resistance  of  the 
circuit  is  known  to  be  1100  ohms,  the  electromotive  force  may  be 
calculated  as  follows  :  — 


or  p  =  CB. 

Then  by  substitution  of  numerical  for  literal  values,  — 
F  =  0.01  ampere  x  1100  ohms  =  11  volts. 

In  order  to  obtain  a  still  clearer  conception  of  the  electric  current, 
let  us  consider  its  analogy  to  a  stream  of  water.  The  electromotive 
force  or  electrical  pressure  corresponds  to  the  pressure  of  the  water, 
the  electrical  resistance  offered  by  the  conductor  of  electricity  to  the 
frictional  resistance  offered  by  the  conductor  of  water,  and  the 
strength  of  the  electric  current  to  that  of  the  current  of  water. 
When  a  certain  current  of  water  is  spoken  of,  it  is  meant  that,  in  a 
unit  of  time,  a  certain  quantity  of  water  passes  through  a  cross 


10 


A   TEXT-BOOK  OF  ELECTRO-CHEMISTRY 


section  of  the  conductor.  A  unit  for  water  currents  has  not  been 
established  for  scientific  use,  but  such  a  current  as  would  cause  one 
cubic  meter  of  water  to  pass  through  a  cross  section  in  one  second 
might,  for  example,  be  considered  to  be  such  a  unit. 

Just  as  we  speak  of  the  quantity  of  water  in  a  water  current,  so 
we  may  also  speak  of  the  quantity  of  electricity  in  the  electric 
current,  without  necessarily  imagining  the  electricity  to  be  of  a 
material  nature.  Accordingly,  when  a  current  of  electricity  of  one 
ampere  is  flowing  in  a  conductor,  it  is  proper  to  say  that  a  unit 
quantity  of  electricity  passes  through  a  cross  section  of  the  conduc- 
tor in  one  second.  This  unit  of  quantity  of  electricity  is  called  the 
coulomb.  The  total  quantity  of  electricity  which  passes  through  a 
cross  section  of  a  conductor  is,  then,  equal  to  the  product  of  the 
current  by  the  time  during  which  the  current  passes.  This  is  ex- 
pressed by  the  following  equation  :  — 

Quantity  of  electricity,  in  coulombs  = 

Current,  in  amperes,  x  Time,  in  seconds. 

In  electrical  science,  it  is  usual  to  .distinguish  between  electro- 
motive force  and  potential  or  voltage  (potential-difference  or 
voltage-difference).  The  term  electromotive  force  is  applied  to  the 
potential-fall  in  a  cell,  which  remains  a  constant  value  as  long  as 
the  cell  remains  constant.  It  may  be  compared  with  the  original, 
constant  pressure  which  forces  a  quantity  of  water  through  a  pipe. 
The  term  potential,  or  voltage,  is  applied  to  the  variable  electrical 
pressure  which  is  found  at  different  points  along  a  conductor.  The 
distinction  between  these  two  terms  will  be  made  clearer  in  the 
following  pages. 

In  most  courses  in  physics,  the   following  experiment  is   per- 
formed:    Water, 
under    a    certain 
pressure,  is  driven 
through  a  narrow, 
horizontal  tube  of 
uniform  bore,  upon 
which  are  a  num- 
ber   of    upright 
•*      manometer   tubes, 
sill  as  shown  in  Fig- 
c  &  b    ure  5 

The    height    of 
the  water  in  each  of  the  upright  tubes  is  a  measure  of  the  pressure 


FORMS  OF  ENERGY  AND   THEIR  MEASUREMENT        11 

with  which  the  water  is  being  driven  through  the  horizontal  tube 
at  that  point.  Considering  the  tube  from  a  to  b,  it  is  seen  that  the 
pressure  of  the  water  decreases  in  a  regular  manner  from  pw  to  p'w, 
and  that  with  the  latter  pressure  the  water  leaves  the  tube.  Cor- 
responding to  the  decrease  in  pressure  along  the  tube  ab,  there  is  a 
decrease  in  the  quantity  of  work  which  can  be  obtained  when  a 
given  quantity  of  water  flows  through  the  tube,  as  will  be  evident 
from  the  following  discussion :  — 

The  quantity  of  work  which  can  be  obtained  from  a  given  quan- 
tity of  water  Qw)  leaving  the  reservoir  at  the  point  a  or  c,  under 
a  pressure  pw  per  square  centimeter,  is  equal  to  Qwpvl.  But  the 
quantity  of  work  which  can  be  obtained  from  the  same  quantity  of 
water  leaving  the  tube  ab  at  6,  under  a  pressure  p'w  per  square 
centimeter,  is  equal  to  Qwp'w.  Hence  the  quantity  of  water  Qv,  in 
moving  through  the  tube  from  a  to  b,  has  decreased  its  power  to  do 
work  from  Qwpw  to  Qwp'w,  and  the  quantity  of  energy  Qwpw  —  Qwp'w, 
or  Qw(pw  —  P'W)  has,  therefore,  been  consumed  in  overcoming  the 
resistance  which  the  tube  offers  to  the  passage  of  the  water.  This 
quantity  of  energy  has  been  changed  into  heat,  which  has  been 
absorbed  by  the  surroundings  'and  consequently  lost.  From  this  it 
is  evident  how  much  depends  upon  the  size  of  the  conducting  tube ; 
for  the  greater  the  size  of  the  tube  the  less  is  the  resistance  which  it 
offers  to  the  passage  of  a  given  quantity  of  water,  and  consequently 
the  greater  the  quantity  of  available  work  at  its  exit. 

Similar  relations  are  found  in  the  case  of  the  electric  current,  as 
will  at  once  be  shown.     Consider  the  wire  AB,  shown  in  Figure  6, 
which  represents  a  com- 
plete electric  circuit  in 
the  form   of  a  straight 
line.     Just  as  the  pres- 
sure   of    the    water    at 
different    points     along 
the  conducting  tube  was 
measured   by  means  of 
upright   manometer 
tubes,  so  the  tension  or 
potential  of  the  electric-    A 
ity  along  the  conducting  Flo 

wire  can  be  measured  by 

an  electrometer,  an  instrument  which  will  be  described  later  on. 
In  this  manner  the  potential  at  the  point  A  (which  is  identical  with 
the  electromotive  force  of  the  circuit)  is  found  to  be  F,  and  at  the 


12  A   TEXT-BOOK  OF   ELECTRO-CHEMISTRY 

point  B  to  be  zero,  when  B  is  connected  to  the  earth  by  a  conductor. 
Furthermore,  just  as  in  the  case  of  the  water  flowing  through  the 
horizontal  tube,  the  quantity  of  work  which  can  be  obtained  at  the 
point  A  from  a  quantity  of  electricity  Q,  at  a  potential  or  under  an 
electrical  pressure  F,  is  equal  to  FQ.  Similarly,  the  quantity  of  work 
which  can  be  obtained  at  the  point  B  from  the  same  quantity  of 
electricity  at  a  potential,  or  under  an  electrical  pressure  PO,  is  equal 
to  FOQ,  or  zero,  since  FO  is  equal  to  zero.  Hence  the  quantity  of 
electricity  Q,  in  flowing  through  the  wire  from  A  to  B,  has  de- 
creased its  power  of  doing  work  from  FQ  to  FOQ,  or  to  zero,  and 
therefore  the  entire  electrical  energy  FQ  has  been  changed  into 
heat  in  overcoming  the  resistance  which  the  wire  offers  to  the  pas- 
sage of  the  electricity.  The  heat  has  disappeared  into  the  sur- 
roundings. The  same  is  true  of  every  electrical  circuit  in  which  no 
work  is  done. 

If  now  work  is  caused  to  be  done,  as,  for  example,  in  the  decom- 
position of  a  solution,  at  some  point  in  the  circuit  almost  the  entire 

electrical  energy  can  be 
transformed  into  useful 

F  work ;  and,  moreover,  it 

is  entirely  immaterial  at 

I  what  point  of  the  circuit 

»  the  work  is  done.    Only 

\  a  small  part  of  the  en- 

\P*  ergy,    depending    upon 

h**--.,. ^  the    material    and    sec- 

tional  area  of   the   cir- 
as 


to 

Flo  7  the  surroundings.   A  cir- 

cuit in  which  the  elec- 
tric energy  is  nearly  completely  transformed  into  work  is  repre- 
sented in  Figure  7,  where  the  wire  circuit  ACB  is  cut  to  admit  the 
electrolytic  cell  at  the  point  C.  Along  the  resulting  circuit  A  to  B 
the  electrometer  gives  the  fall  in  potential  as  represented  in  the 
figure  by  the  dotted  line,  showing  that  the  fall  takes  place  almost 
entirely  where  the  work  is  being  done  in  decomposing  the  solution. 
The  fall  in  potential  in  the  same  circuit  when  but  one  half  of  the 
total  electrical  energy  FQ  is  transformed  into  work  is  represented  in 
Figure  8. 

It  is  evident,  then,  that,  in  an  electric  circuit,  electrical  energy  may 
be  entirely  transformed  into  heat,  or  into  varying  proportions  of  heat 
and  work,  depending  upon  the  nature  and  arrangement  of  the  circuit. 


FORMS  OF   ENERGY  AND   THEIR  MEASUREMENT         13 


In  an  entirely  analogous  manner,  the  energy  possessed  by  the 
water,  in  the  case  already  considered,  may  be  almost  entirely  trans- 
formed into  heat  as  has 
been  shown,  or  it  may  be 
almost  entirely  trans- 
formed into  work,  for, 
if  the  tube  be  closed  at 
the  point  5,  the  pres- 
sure at  that  point  at 
once  rises,  as  shown  in 
Figure  9,  from  p'w  to  pw 

and  the  maximum  quan-      '  ^ 

C 


B 

toekrth 


FIG.  8 


tity  of  energy,  pwQw, 
may  then  be  obtained 
at  b  and  transformed 
into  work  as  desired.  The  current  of  water  differs  from  the  cur- 
rent of  electricity  in  that  the  former  may  leave  its  conductor  while 
still  in  possession  of  a  certain  amount  of  kinetic  energy.  This 
property  is  not  possessed  by  the  latter  current. 


FIG.  9 


The  fall  of  potential  throughout  any  galvanic  circuit  may  be  pre- 
sented by  the  method  just  employed.  If  no  work  is  done  in  the  cir- 
cuit and  if  the  resistance  of  the  circuit  is  uniform  throughout,  the 
potential  falls  regularly  from  its  highest  value  at  one  end  to  its  low- 
est value,  zero,  at  the  other,  as  represented  in  Figure  6.  If,  however, 
work  is  done  at  some  point  in  the  circuit  requiring  a  certain  quantity 
of  electrical  energy  and  consequently  a  certain  potential,  the  poten- 
tial falls  by  a  definite  amount  at  the  point  where  the  work  is  done. 
Supposing  this  fall  in  potential  to  be  equal  to  F,  then  the  remaining 
potential  F  —  F'  decreases  regularly  throughout  the  rest  of  the  circuit 


14  A   TEXT-BOOK  OF   ELECTRO-CHEMISTRY 

as  represented  in  Figure  7.     If,  finally,  the  circuit  does  not  possess 
the  same  resistance  in  every  part,  the  fall  in  potential  in  each  part  is 

proportional  to  its  resist- 
ance.  Consider,  for  in- 
stance,  the  circuit  rep- 
resented  in  Figure  10, 


8 


4 

t 


\ 


\  where  the  resistance  of 

\  AB  is  twice  as  great  as 

-j.-_  ---'  that  of    BC  and   four 


Ts 

x>~  times  as  great  as  that 

of  CD. 

As  shown  in  the  fig- 
o  ure,  the  fall  in  potential 

A  B  C  JD  along  AB  is  twice  as 

_       ..  ^*      great  as  tnat  along  JDO,. 

F IG.  10  . 

and  tour  times  as  great 

as  that  along  CD.  This  relation  between  the  fall  in  potential  in  a 
conductor  and  its  resistance  follows  of  necessity  from  Ohm's  law, 
which  holds  for  the  whole  circuit  as  it  does  for  each  part,  as  will 
now  be  shown.  In  applying  the  equation  which  expresses  Ohm's 
law, — 


.to  any  part  of  a  circuit,  the  value  of  P  is  the  difference  of  potential 
between  the  two  ends  of  that  part,  and  the  value  of  R  is  the  resistance 
of  the  part.  Hence  in  the  case  represented  by  Figure  10  the 
following  equations  are  true,  since  the  current  is  the  same  through- 
out the  circuit,  whatever  the  arrangement  of  the  resistances  of  the 
parts,  as  in  the  case  of  a  current  of  water  flowing  through  a  series 
of  tubes  of  varying  diameters :  — 

_P-FO_F-FI  ,  P!-F2  ,  F2-F3 

o  — — ~t~ — \~ •  — y 

R  R!  R2  R3 

where  F  —  FO  =  (F  —  FX)  -f-  (FI  —  F2)  +  (p2  —  F3)  and  R  =  R!  -f  R2 -f  R3. 

It  follows  from  the  equations  that  the  potential-difference  between 
the  single  points  must  be  proportional  to  the  corresponding  resist- 
ances. Whether  the  resistance  in  the  circuit  is  that  of  a  metallic, 
or  of  a  liquid,  conductor,  such  as  a  salt  solution,  or  that  of  a  com- 
bination of  both  kinds  of  conductors,  this  statement  is  still  true. 

If,  in  a  galvanic  cell,  the  poles  be  connected  by  a  wire,  the  total 
resistance  of  the  circuit  consists  of  that  of  the  wire,  called  the  ex« 


FORMS  OF  ENERGY  AND  THEIR  MEASUREMENT   15 

ternal  resistance,  and  that  of  the  liquid,  or  liquids,  of  the  cell  (for 
instance  in  case  of  the  Daniell  cell,  that  of  the  zinc  sulfate  and 
copper  sulfate  solutions),  called  the  internal  resistance.  If,  now, 
the  external  resistance  of  a  Daniell  cell  is  1000  ohms,  and  the  internal 
resistance  is  100  ohms,  while  the  electromotive  force  of  the  cell  is 
1.10  volts,  it  follows  from  the  above  discussion  that  the  potential- 
fall  in  the  external  part  of  the  circuit,  the  wire,  is  1.00  volt  and  in 
the  internal  part  of  the  circuit,  the  solution,  is  0.10  volt.  It  is  evi- 
dent that  there  is  a  difference  between  the  electromotive  force  of  a 
cell  and  the  potential-fall  in  the  external  part  of  its  circuit,  being  in 
the  Daniell  cell,  just  considered,  1.10  and  1.00  volts,  respectively.  If 
F  denotes  the  electromotive  force  of  the  cell,  F!  and  RI?  the  potential- 
fall  and  the  resistance  in  the  internal  circuit,  F2  and  B2,  the  potential- 
fall  and  the  resistance  in  the  external  circuit,  then  the  following 
relation  exists  between  these  quantities  :  — 

F  =  F!  +  F2, 

R 

then  Z 


F2  F2  R2 

From  this  relation  it  follows  that  the  greater  the  external  resistance 

R2,  the  more  nearly  the  fraction  Rl  +  R2  approaches  the  value  one,  and 

Ra 

hence  the  more  nearly  the  potential-fall  in  the  external  circuit  F2 
approaches  the  electromotive  force  of  the  cell  F.  If  the  external 
resistance  is  made  infinitely  great  by  breaking  the  external  circuit, 
these  two  quantities,  F2  and  F,  become  identical  ;  for  on  the  open  cir- 
cuit there  can  never  be  a  fall  in  potential,  since  this  can  only  take 
place  when  current  flows,  transforming  electrical  energy  into  heat  or 
into  heat  and  work.  Except  when  the  external  resistance  is  made 
infinite  by  breaking  the  circuit,  the  potential-fall  in  the  external  cir- 
cuit is  always  less  than  the  electromotive  force  of  the  cell,  but 
approaches  the  latter  as  the  external  resistance  approaches  infinity 
or  the  internal  resistance  approaches  zero. 

The  Electrical  Equivalent  of  Heat.  —  From  its  analogy  to  the 
expression  for  the  mechanical  energy  of  water  pwQw,  it  has 
been  assumed  that  the  expression  FQ  represents  electrical  energy, 
it  being  the  product  of  the  quantity  of  electricity  by  its  "pres- 
sure" or  potential.  If  the  correctness  of  this  assumption  be 
questioned,  it  is  easily  possible  to  prove  it  to  be  correct  by 
direct  experiment,  and,  at  the  same  time,  to  calculate  the  electrical 
equivalent  of  heat.  Let  us  consider,  first,  a  circuit  in  which  there 


16  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

exists  an  electromotive  force  F,  expressed  in  volts,  or,  in  other 
words,  a  circuit  in  which  there  is  a  fall  of  potential  from  F  to  0.  It 
may  here  be  mentioned  that  the  beginner  is  inclined  to  fall  into 
error  through  the  former  expression  by  assuming  that  the  value  of 
F  remains  constant  throughout  the  circuit,  which,  as  seen  from  the 
latter  expression,  is  not  at  all  the  case.  The  resistance  of  the  cir- 
cuit is  so  chosen  that  in  one  second,  the  quantity  of  electricity  Q,  ex- 
pressed in  coulombs,  passes  through  a  cross  section  of  the  conductor. 
Since  the  quantity  of  electricity  passing  through  a  cross  section  in 
one  second  is  equal  to  the  current,  expressed  in  amperes,  this  is 
equivalent  to  saying  that  a  current  of  Q  amperes  is  flowing  through 
the  conductor.  If  now  the  current  performs  no  work  in  the  circuit, 
the  entire  quantity  of  electrical  energy  is  transformed  into  heat. 
Hence  the  quantity  of  heat  generated  in  one  second  when  the  entire 
circuit  is  placed  in  a  calorimeter  is  equivalent  to  the  quantity  of 
electrical  energy  which  disappears  in  the  same  time,  or  is  equivalent 
to  the  product  FQ,  under  the  assumption  that  this  product  correctly 
represents  the  electrical  energy. 

Let  us  consider,  next,  a  circuit  in  which  an  electromotive  force  ^  F 
exists,  causing  a  current  of  two  amperes  to  flow  through  it.  The 
quantity  of  heat  which  would  be  generated  in  one  second  in  a  calo* 
rimeter  containing  this  circuit  should  be  the  same  as  in  the  former 
case,  since 

£F  x  2Q  =  FQ. 

Similarly,  under  the  above  assumption,  whenever  the  electromotive 
force  and  current  in  any  circuit  have  such  values  that  their  product 
is  equal  to  FQ,  the  same  quantity  of  heat  should  be  generated  in  a 
given  time  in  a  calorimeter  containing  the  circuit,  for  the  same  quan- 
tity of  electrical  energy  would  in  each  case  disappear.  Experiment 
has  shown  that  this  is  actually  the  case.  Moreover,  if  the  resistance 
of  the  circuit  is  such  that,  with  an  electromotive  force  of  2  F  volts, 
the  same  current,  Q  amperes,  is  produced,  then,  since  the  product 

2  F  x  Q  =  2  FQ, 

twice  as  much  heat  should  be  generated  in  one  second  as  in  the  for- 
mer cases,  and  so  forth.  Experiment  has  proven  this  also  to  be  true. 
Therefore  the  product  FQ  does  represent  correctly  the  quantity  of 
electrical  energy. 

The  calculation  of  the  electrical  equivalent  of  heat  is  now  very 
simple.  The  unit  of  electrical  energy  is  naturally  the  product  of 
one  volt  by  one  coulomb,  or  one  volt-coulomb.  It  is  only  necessary 


FORMS  OF   ENERGY  AND  THEIR  MEASUREMENT        17 

to  measure  the  heat  generated  when  one  coulomb  of  electricity  is 
forced  through  a  circuit  by  an  electromotive  force  of  one  volt,  or 
expressed  differently,  when  one  coulomb  of  electricity  undergoes  a 
fall  in  potential  of  one  volt.  The  resistance  of  the  circuit  does  not 
enter  into  consideration,  because  the  quantity  of  energy  is  indepen- 
dent of  the  time  and  because  the  resistance  only  determines  the  time 
required  for  the  fall  to  take  place.  If  this  quantity  of  heat  is  x 

calories,  -  is  the  electrical  equivalent  of  heat,  and  represents  the 
x 

number  of  units  of  electrical  energy  which  are  equivalent  to  one  unit 
of  heat  energy. 

TJie  electrical  equivalent  of  heat  has  been  found  to  be  :  — 

1  volt-coulomb  =  0.2387  calorie, 
or  4.189  volt-coulombs  =  1  calorie. 

The  mechanical  equivalent  of  electricity  is  easily  calculated  from 
the  mechanical  and  the  electrical  equivalents  of  heat. 

Since  42720  gram-centimeters  =  1  calorie, 

then  1  volt-coulomb  =  10198  gram-centimeters, 

which  is  the  mechanical  equivalent  of  electricity. 

The  quantity  of  electrical  energy  which  is  available  when  a  quan- 
tity of  electricity  Q  is  forced  through  a  wire  by  an  electromotive 
force  F  is  equal  to  FQ.  If  this  energy  is  completely  transformed 
into  heat,  then 

FQ  =  k  x  Q,  (1) 

when  Q  is  the  total  quantity  of  heat  generated  and  fc  is  a  factor 
which  depends  on  the  ratio  existing  between  the  units  in  which  the 
two  forms  of  energy  are  expressed.  If  the  corresponding  current  is 
represented  by  c,  then 

FC  =  7c  x  q,  (2) 

where  q  is  the  quantity  of  heat  generated  in  a  unit  of  time.  But 
according  to  Ohm's  law 

c  =  Jc'  x  -,  (3) 


or  F  =  &'RC  ;  (4) 

then  by  substitution  of  this  value  of  F  in  the  equation  (2), 


we  get  cW  =  k  •  q  ;      or  if      =  Jc", 


c2B  =  k"  -  q.  (5) 


18  A   TEXT-BOOK  OF   ELECTRO-CHEMISTRY 

The  last  equation  may  be  expressed  in  words  as  follows  :  The  heat 
energy  generated  in  the  whole  or  in  a  part  of  a  circuit  is  proportional 
to  the  resistance  involved  and  to  the  square  of  the  current.  This  law 
was  discovered  by  Joule  in  1841  and  is  known  as  Joule's  law.  Its 
experimental  verification  is  a  further  proof  of  the  validity  of  Ohm's 
law.  If  the  quantities  c,  R,  and  Q  are  expressed  in  amperes,  ohms, 
and  calories,  respectively,  then  the  number  of  calories  generated  in 
one  second  is  given  by  the  equation,  — 

0.2387  x  amperes2  x  ohms  =  calories. 

The  following  facts  may  also  be  of  interest  to  the  readers :  — 
1  joule  =  107  ergs  =  1  volt-coulomb. 

A  certain  number  of  joules,  then,  denotes  a  certain  quantity  of 
energy  independent  of  the  time.  If  the  quantity  of  energy  supplied 
to  a  machine  in  a  given  time  is  divided  by  this  time,  expressed  in 
seconds,  the  quotient  is  the  quantity  of  energy  supplied  in  one 
second  and  is  called  the  power  of  the  machine.  The  unit  of 
power, 

1  volt-ampere  =  1  watt  =  1  joule  per  second. 

The  following  equations  give  the  relations  between  the  electrical 
units  of  power  :  — 

Watts  =  0Joalef  =  Volt-coulombs  =  Volt.          es. 

Seconds  Seconds 

The  power  multiplied  by  the  time  in  seconds  gives  again  the  en- 
ergy supplied  during  this  time.  Hence  the  equations, 

1  watt-second  =  1  joule 
and  1  watt-hour     =  3600  joules. 

In  technical  work  the  watt-hour  or  kilo-watt-hour  is  generally  used 
for  the  measurement  of  power  instead  of  joule  or  kilo-joule,  and  the 
ampere-hour  instead  of  the  coulomb,  for  the  measurement  of  quantity 
of  electricity.  It  may  be  mentioned  that  1  ampere-hour  equals  3600 
coulombs. 

A  table  showing  the  relation  between  the  energy  units  most  fre- 
quently used  may  be  found  at  the  end  of  the  book. 

The  Electrical  Furnace  and  its  Industrial  Importance.  —  An  exact 
knowledge  of  the  relation  between  electrical  energy  and  heat  which 
has  just  been  considered  is  of  great  importance  both  in  pure  science 
and  in  technical  work.  If  it  is  desired  to  obtain  very  high  tempera- 


FORMS  OF  ENERGY  AND  THEIR  MEASUREMENT    19 

tures,  from,  say,  1500°  to  3000°  and  higher,  as,  for  instance,  in  the 
manufacture  of  calcium  carbide  from  calcium  oxide  and  charcoal 
according  to  the  equation, 

CaO  +  30  =  CaC2  +  CO, 

it  often  happens  that  electrical  heating  is  the  only  method  of  heat- 
ing by  which  the  required  temperature  can  be  reached,  or  by  which 
commercially  favorable  conditions  can  be  obtained.  The  apparatus 
in  which  such  processes  are  allowed  to  take  place  is  called  an  "  elec- 
tric furnace." 

One  method  of  heating,  which  will  be  considered  in  detail,  con- 
sists in  leading  two  insulated  ends  of  a  circuit  through  two  opposite 
sides  of  the  furnace  and  connecting  them  inside  the  furnace  by 
means  of  a  rod  of  material  of  great  resistance,  such  as  carbon.  The 
resistance  of  this  rod  should  be  much  greater  than  that  of  the  ends 
of  the  circuit  leading  into  the  furnace ;  since  the  greater  the  ratio 
of  the  internal  to  the  external  resistance,  the  better  the  utilization  of 
the  electrical  energy  in  the  furnace.  By  means  of  this  arrangement 
it  is  possible,  in  a  very  small  space,  to  convert  practically  the  entire 
electrical  energy  supplied  to  the  furnace  into  heat  which  is  imparted 
to  the  reaction  mixture  packed  around  the  rod.  The  high  tempera- 
ture attainable  is  only  limited  by  the  inertness  and  stability  of  the 
material  of  the  high  resistant  conductor.  The  utilization  of  the 
heat  is  excellent,  since  the  heating  is  done  from  the  interior.  In 
order  to  illustrate  the  thermal  effect  of  the  electric  current,  the 
following  numerical  example  is  given. 

Let  us  consider  that  an  electromotive  force  of  100  volts  is  avail- 
able and  that  the  resistance  of  the  circuit  outside  of  the  furnace  is 
0.001  of  an  ohm.  If  now  the  circuit  be  completed  by  means  of  an 
inner  furnace  resistance  of  0.999  ohm,  then,  since  the  total  resist- 
ance of  the  circuit  is  equal  to  0.10  ohm,  according  to  Ohm's  law, 

0=?, 

R 


or  c  =  =  1(X)()  res. 

0.10  ohm 

Since  the  potential-fall  in  the  two  parts  of  the  circuit  is  propor- 
tional to  the  respective  resistances,  then  there  will  be  a  potential 
fall  of  one  volt  along  the  circuit  outside,  and  of  99  volts  along  the 
circuit  inside  of  the  furnace.  Hence  99  per  cent  of  the  available 
electrical  energy  is  transformed  into  heat  in  the  furnace.  The 


20 


A  TEXT-BOOK  OF   ELECTRO-CHEMISTRY 


number  of  calories  of  heat  generated  per  second  is  easily  found  by 
either  of  the  following  two  methods :  — 

Method  A. 

1  watt-second  =  1  joule  =  0.2387  calorie 

Watt-seconds  =  Volts  x  Amperes  =  99  X  1000  =  99,000. 

Then  the  heat  generated  in 
calories  per  second  =  99,000  x  0.2387  =  23,631. 
Method  B. 


Amperes   x  Ohms  x  Seconds  =  calories  X  0.2387. 


or 


1  ampere  -ohm-second  =  0.2387  calorie. 
Number  of  ampere2-ohm-seconds  =  10002  x  0.099  =  99,000. 
Hence  number  of  calories  per  second=99,000  x  0.2387  =23,631. 

If  the  quantity  of  heat  is  too  great,  less  electrical  energy  can  be 
taken  from  the  current  source  by  increasing  the  resistance  inside  of 
the  furnace.  At  the  same  time,  the  electrical  energy  is  thus  better 
utilized,  since  the  utilization  increases  with  the  value  of  the  ratio  of 
the  internal  to  the  external  resistance.  The  quantity  of  heat  re- 
quired in  any  given  case  naturally  depends  upon 
the  heat  of  reaction,  the  heat  capacity  of  the  sub- 
stances, and  the  loss  of  heat  by  conduction  and 
radiation.  For  commercial  work  electric  furnaces 
are  now  built  with  a  capacity  of  1000  kilowatts  and 
over,  to  be  operated  with  a  voltage  of  50  volts  and 
a  current  of  20,000,  or  more,  amperes. 

The  internal  resistance  is  very  often  replaced  by 
FIG.  11  an  electric  arc,  especially  if  it  is  desired  to  concen- 

trate the  heating  on  a  small  surface.  The  calculation  of  the  heat 
effect  thus  obtained  is  similar  to  the  calculation  in  the  example  just 
considered.  It  requires  only  that  the  potential  difference  between 
the  two  poles  and  the  current  be 
known.  Even  in  the  case  of  the  elec- 
tric arc,  it  cannot  be  assumed  that  the 
temperature  is  higher  than  3500°  ty 
since  at  that  temperature  the  carbon 
itself  begins  to  vaporize.  The  glow- 
ing gas  of  the  arc,  can,  however,  be 
brought  to  a  considerably  higher  temperature. 

Models  of  the  electrical  resistance  furnace  of  Borchers  and  of  the 


FIG.  12 


FORMS  OF  ENERGY  AND  THEIR  MEASUREMENT         21 

electric  arc  furnace  of  Heroult  are  shown  in  Figures  12  and  11, 
respectively.  These  furnaces  are  on  the  market  in  a  great  variety 
of  forms. 

Since  in  technical  work  the  economy  of  a  process  is  of  first 
importance,  electro-chemical  industry  has  developed  mostly  in  the 
direction  of  such  processes  as  may  be  carried  out  in  the  electric, 
furnace.  These  processes  are  carried  out  to  advantage  when  elec- 
trical energy  may  be  had  at  a  price  of  about  one  quarter  of  a  cent  per 
kilowatt-hour  and  under.  Thus  during  the  last  ten  or  twenty  years 
enormous  works  have  been  established  in  the  United  States  of  North 
America  (especially  at  the  Niagara  Falls),  in  France,  in  Switzer- 
land, and  in  Norway,  which  daily  transform  many  millions  of 
meter-kilograms  into  chemical  energy  by  means  of  the  electric  cur- 
rent. In  order  to  give  the  reader  an  idea  of  the  magnitude  and 
commercial  importance  of  these  works,  their  products  and  the  im- 
portance of  them  will  be  briefly  considered. 

Most  of  the  processes  carried  out  in  electric  furnaces  involve  the 
reduction  of  oxides  by  carbon.  Borchers  was  the  first  to  state  that 
in  the  electric  furnace  all  oxides  could  be  reduced  by  carbon  at  a 
sufficiently  high  temperature.  As  a  result  of  this  reduction  with 
carbon,  pure  metal  is  not  necessarily  formed,  for  carbon  compounds 
of  the  metal  may  instead  be  formed. 

This  is  the  case  in  the  preparation  of  calcium  carbide,  which  is 
made  on  a  very  large  scale  to  be  used  in  turn  for  the  preparation  of 
acetylene  gas.  Calcium  carbide  is  of  great  interest  also  from 
another  point  of  view.  Under  certain  circumstances  it  is  capable  of 
uniting  with  atmospheric  nitrogen  to  form  calcium  cyanamide  ac- 
cording to  the  equation, 

CaC2  +  N2  =  CaCN2  -f  C, 

and  the  latter  compound  when  treated  with  steam  under  pressure  is 
decomposed  with  the  formation  of  ammonia.  This  decomposition 
is  represented  by  the  equation, 

CaCN2  +  3  H20  =CaC03  +  2  NH3. 

On  the  other  hand,  when  calcium  cyanamide  is  leached  with  hot 
water  and  the  calcium  hydroxide  formed  is  filtered  off,  the  finely 
crystallizing  substance,  dicyandiamide,  is  obtained  upon  cooling. 
The  reaction  is  as  follows :  — 

2  CaCN2  +  4  H20=  2  Ca(OH)2  +  (CN2H2)2. 
By   fusion  with  soda,  dicyandiamide  is   transformed  into  sodium 


22  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

cyanide  and  ammonia  together  with  small  quantities  of  tricyan- 
triamide  (CN2H2)3.  Even  the  latter  compound  can  also  be  trans- 
formed into  sodium  cyanide  and  ammonia. 

The  reactions  just  described  are  of  great  importance  because  they 
furnish  a  means  of  transforming  atmospheric  nitrogen  into  a  form 
which  can  be  utilized.  In  view  of  the  threatened  exhaustion  of  the 
great  saltpeter  deposits,  this  importance  is  not  to  be  undervalued. 

A  further  advance  in  the  domain  of  nitrogen  fixation  has  been 
made  by  so  conducting  <  the  processes  that  calcium  cyanamide  is 
obtained,  although  not  quantitatively,  from  calcium  carbonate, 
carbon,  and  atmospheric  nitrogen,  without  the  necessity  of  forming 
calcium  carbide  as  an  intermediate  product.  The  following  reaction 
is  involved :  — 

CaO  +  2  C  +  N2  =  CaCN2  4-  CO. 

The  conglomerate,  containing  the  calcium  cyanamide,  gives  on 
analysis  from  12  to  14  per  cent  of  nitrogen.  By  experiment  it  has 
been  shown  to  be  a  good  fertilizer,  capable  of  being  used  on  the  soil 
in  its  original  form. 

Besides  calcium  carbide,  silicon  carbide  (carborundum),  valued 
especially  as  an  abrasive  substance,  is  prepared  on  a  large  scale  in 
this  way.  The  following  reaction  is  involved :  — 

Si02  +  3C  =  SiC+2CO. 

Various  alloys  are  prepared  in  the  electric  furnace  by  the  reduc- 
tion of  certain  minerals.  For  instance,  when  chrome-iron  ore 
(FeO  •  Cr203)  is  heated  with  sufficient  carbon  an  iron-chromium  alloy 
results,  containing  over  sixty  percentage  of  chromium.  In  a  similar 
manner  an  iron-titanium  alloy,  containing  a  proportion  of  titanium 
varying  with  the  conditions  of  preparation,  may  be  prepared  from 
Ilminite  (FeO-Ti02). 

These  alloys  are  used  in  the  production  of  steel,  etc.,  in  order  to 
obtain  a  definite  chromium  or  titanium  content. 

Electrical  heating  is  also  used  to  advantage  in  the  production  of 
phosphorus  by  heating  mixtures  of  the  natural  phosphates  (chiefly 
calcium  phosphate)  with  carbon  and  quartz  or  kaolin.  The  follow- 
ing reaction  takes  place  :  — 

Ca3(P04)2  +  3  Si02  +5C=2P+3  CaSi03  +  5  CO. 

The  phosphorus  which  distills  off  from  the  mixture  is  collected 
under  water. 

Recently,  carbon  bisulfide  has  been  prepared  from  pieces  of  sul- 
fur and  carbon  in  an  electric  furnace. 


FORMS  OF  ENERGY  AND  THEIR  MEASUREMENT    23 

Finally,  it  may  be  mentioned  that  the  preparation  of  the  nitrogen 
oxides  by  the  action  of  the  electric  arc  upon  air  has  recently 
received  increased  attention.1  The  air  is  forced  past  an  electric  arc 
formed  by  an  alternating  current,  becoming  highly  heated  and 
forming  a  small  quantity  of  the  nitrogen  oxides.  Before  these 
oxides  can  decompose  to  any  considerable  extent,  they  are  rapidly 
cooled  to  ordinary  temperatures. 

In  all  of  these  processes,  the  number  of  which  might  easily  be 
increased,  the  electric  current  exerts  only  a  heating  effect.  The 
electric  furnace  is,  however,  also  used  in  processes  in  which  the 
current  is  a  direct  one  and  exerts  both  an  electro-thermic  and  an 
electrolytic  action,  as,  for  example,  in  the  process  for  the  prepara- 
tion of  metallic  aluminium.  In  this  case,  the  current  furnishes  the 
heat  required  to  maintain  the  fusion  and  also  decomposes  the  alu- 
minium compounds  dissolved  in  it  with  the  separation  of  metallic 
aluminium  at  the  cathode. 

Dark  or  Silent  Electrical  Discharge.  —  The  mutual  discharge  of 
two  oppositely  charged  bodies,  when  they  are  separated  by  air  or  any 
other  dielectric,  takes  place  in  various  ways  according  as  the  poten- 
tial-difference, the  distance,  and  the  form  of  the  bodies  is  varied. 
It  can  take  place  in  the  form  of  a  dark  or  so-called  silent  discharge 
accompanied  by  faintly  visible  streamers  of  light.  Such  a  discharge 
differs  from  the  familiar  electric  arc  in  that  in  the  former  case  the 
passage  of  electricity  takes  place  only  through  the  gas  separating 
the  two  electrodes,  while  in  the  latter  case  it  takes  place  chiefly 
through  the  vapors  formed  from  the  electrodes.  If,  in  the  latter 
case,  a  constant  potential-difference  is  maintained,  the  conductance 
of  the  electrode  vapors  increases  greatly  both  the  current  intensity 
and  the  quantity  of  electrical  energy  which  in  the  unit  of  time  is 
transformed  into  heat. 

If  the  potential-difference  between  the  two  electrodes  is  increased 
successively,  the  non-luminous  discharge  through  gases  becomes 
finally  an  electric  arc.  Under  the  usual  circumstances,  as  soon  as 
this  transformation  takes  place,  the  current  suddenly  increases  to  a 
high  value  while  the  potential-difference  sinks  considerably.  It  is, 
in  general,  not  possible  to  utilize  the  high  potential-difference 
obtainable  by  very  powerful  machines,  since  the  current  would  in- 
crease to  such  an  extent  as  to  cause  even  the  most  non-volatile 
electrodes  to  volatilize.  Nevertheless  under  certain  conditions  all 

1  For  further  particulars  see  J.  Erode,  "  Oxydation  des  Stickstoffs  in  der 
Hockspannungs  flamme.  Habilitationsschrift,  Karlsruhe"  (1905),  W.  Knapp, 
publisher,  Halle,  Saxony. 


24  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

possible  transition  phenomena  between  discharge  through  gases  and 
through  the  electric  arc  can  be  produced,  as,  for  instance,  when  the 
electric  current  is  transmitted  chiefly  by  means  of  the  electrode 
vapor  near  the  electrode,  and  undergoing  a  gradual  transition  into 
purely  a  discharge  through  gases  at  greater  distances.1  It  would 
be  more  correct  to  characterize  the  electric  arc  (which,  in  the  case  of 
the  preparation  of  the  nitrogen-oxygen  compounds  as  just  described, 
appears  as  a  quietly  burning  flame)  as  a  case  of  discharge  through 
gases.  In  the  case  of  alternating  currents,  even  with  those  of  high 
frequency,  the  discharge  is  naturally  discontinuous.  It  is  in  fact 
possible  that  every  discharge  is  discontinuous.  This  is  certainly 
true  of  spark  discharges,  which  may  be  considered  to  be  electric 
arcs  of  exceedingly  short  duration.  During  such  discharges  the 
current  rises  to  enormous  values.  That,  in  this  case,  the  vapor  of 
the  electrodes  plays  a  part  in  the  conduction  of  the  electricity,  is 
shown  by  spectroscopic  observations,  and  also  by  the  fact  that  if 
sparks  are  allowed  to  pass  between  electrodes  of  the  noble  metals 
under  water,  colloidal  solutions  are  formed. 

As  already  indicated,  silent  discharges  (and  also  spark  dis- 
charges) may  exert  a  chemical  influence  on  gases.  Thus,  to  a  cer- 
tain extent,  hydrogen  and  nitrogen  are  made  to  combine  to  form 
ammonia,  hydrogen  and  cyanogen  to  form  hydrocyanic  acid,  carbon 
monoxide  and  water  to  form  formic  acid,  and  oxygen  to  be  trans- 
formed into  ozone.  In  one  respect  this  last  technically  important 
reaction  is  very  remarkable.  While  in  all  the  other  applications  of 
the  alternating  current  which  have  been  mentioned,  only  the  quan- 
tity of  heat  or  the  temperature  attainable  entered  into  consideration, 
in  this  case  it  appears  that  the  form  of  the  current  must  be  consid- 
ered. According  to  the  investigations  of  Warburg,2  a  close  rela- 
tionship exists  between  the  nature  of  the  light  at  the  points  of  the 
conductors  and  the  yield  of  ozone.  It  is  very  probable  that  the  for- 
mation of  ozone  should  be  attributed  to  photo-  or  cathodo-cheniical 
action.  It  is  also  interesting  to  note  that  Warburg  found  that,  for 
the  form  of  discharge  used  by  him,  the  direct  excels  the  alternating 
current. 

When  the  ozone  has  reached  a  certain  concentration,  it  ceases  to 
be  formed. 

Electrical  Capacity.  —  It  may  be  well  at  this  point  to  explain  the 
term  electrical  capacity,  although  it  has  more  to  do  with  static  elec- 

1  See  also  O.  Lehmann,  **  Elektrische  Lichterscheinungen  und  Entladungen," 
W.  Knapp,  Halle,  Saxony  (1898). 

2  Drude's  Annalen,  12,  988  (1904)  ;  17,  1  (1905). 


FORMS  OF  ENERGY  AND  THEIR  MEASUREMENT    25 

tricity  than  with  our  present  subject.  It  is  to  be  especially  noted 
that  this  so-called  electrical  capacity  is  quite  distinct  from  the  ca- 
pacity factor  of  .electrical  energy,  or  the  quantity  of  electricity.  By 
electrical  capacity  is  meant  the  capacity  of  a  body  for  taking  up 
or  holding  electricity.  This  capacity  of  a  body  is  independent  of 
its  material  content,  but  dependent  on  its  size,  form,  temperature, 
and  surroundings.  If  two  bodies  of  unequal  electrical  capacities  be 
charged  with  the  same  quantity  of  electricity,  the  potential  of  the 
two  charges  will  be  unequal,  and,  further,  it  will  be  higher  on  the 
body  of  least  capacity.  If  these  two  bodies  be  charged  with  such 
quantities  of  electricity  that  the  two  charges  are  at  the  same  poten- 
tial, the  two  quantities  of  electricity  will  be  unequal,  and  the  larger 
quantity  will  be  on  the  body  of  greatest  capacity.  The  electrical 
capacity  is  also  denned  by  the  following  equation  :  — 

Electrical  capacity  (*,)  =  Quantity  of  electricity  (Q) 

Potential  (F) 

The  unit  of  capacity  is  called  the  farad,  and  is  denned  to  be  the 
electrical  capacity  of  a  body  upon  which  a  charge  of  electricity  of 
one  coulomb  possesses  a  potential  of  one  volt.  The  above  equation 
may  therefore  be  written  as  follows :  — 

Q.  in  coulombs 

ke.  in  farads  =  — — : , 

F,  in  volts 

Positive  and  Negative  Electricity.  The  Electrometer. — Thus  far 
we  have  considered  the  electric  current  as  analogous  to  the  water 
current.  This  analogy  is  especially  useful  to  beginners,  as  it  serves 
to  facilitate  the  comprehension  of  electrical  phenomena.  It  is,  how- 
ever, not  a  perfect  one,  and  care  must  be  taken  to  prevent  misguid- 
ances ;  for  an  electric  current  is  not  as  simple  as  a  current  of  water. 

If  a  solution  of  copper  chloride  be  introduced  into  a  circuit  as 
previously  described,  it  is  observed  that,  while  copper  is  separating 
at  one  of  the  pieces  of  platinum,  chlorine  is  separating  at  the  other. 
If  now,  from  these  facts,  it  is  conceived  that  the  copper  is  trans- 
ported through  the  solution  to  one  electrode,  then  it  must  also  be  con- 
ceived that  the  chlorine  is  transported  in  the  opposite  direction  to  the 
other  electrode.  From  this  movement  of  ponderable  matter  in  two 
opposite  directions  by  means  of  the  electric  current,  it  must  be 
assumed  that  the  electric  current,  unlike  the  water  current,  simul- 
taneously possesses  two  opposite  directions.  But  we  know  from  the 
science  of  static  electricity  that  we  have  to  distinguish  between  two 


26  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

kinds  of  electricity,  called  respectively  positive  and  negative  elec- 
tricity. Hence  it  may  well  be  concluded  that  the  electric  current 
consists  of  simultaneous  motions  of  positive  electricity  with  copper 
particles  in  one  direction  and  of  negative  with  chlorine  particles  in 
the  other.  This  conclusion  is  supported  by  the  electrometric  experi- 
ments to  be  described  later. 

The  conditions  in  the  case  of  electrical  energy  differ,  then,  some- 
what from  those  in  the  case  of  mechanical  energy,  as  will  now  be 
shown.  The  product,  volume  by  pressure,  has  been  shown  to  repre- 
sent a  quantity  of  mechanical  energy.  The  capacity  factor,  the  vol- 
ume, is  always  a  positive  quantity,  since  but  one  kind  of  volume  is 
known.  The  product,  quantity  of  electricity  by  electromotive  force, 
has  also  been  shown  to  represent  a  quantity  of  electrical  energy. 
In  this  case,  the  capacity  factor,  the  quantity  of  electricity  Q,  may 
be  either  positive  or  negative.  For  these  two  kinds  of  capacity  fac- 
tors, -f  Q  and  —  Q,  we  have  the  following  laws :  Whenever  a  quantity 
-f  Q  combines  with  an  equivalent  quantity  —Q,  a  zero  quantity  always 
results.  Whenever  a  quantity  of  positive  electricity  is  produced,  there  is 
always  produced  at  the  same  time  an  equivalent  quantity  of  negative 
electricity;  and  when  these  two  quantities  of  electricity  are  brought 
together  again,  they  completely  neutralize  each  other. 

In  the  study  of  electrical  phenomena,  it  is  necessary  to  become 
accustomed  to  abstract  thinking.  It  cannot  be  expected  that  a  quan- 
tity of  electricity  can  be  made  as  tangible  to  us  as  a  quantity  of 
matter.  Upon  closer  consideration  it  will  be  seen,  moreover,  that  if 
the  term  matter  is  intelligible  there  is  no  reason  why  the  term  elec- 
tricity or  quantity  of  electricity  should  be  unintelligible.  Let  us 
first  understand  clearly  what  is  understood  by  the  term  matter.  We 
speak  of  matter  when  we  recognize  a  certain  number  of  properties  in 
a  given  place.  One  of  these  properties  is  the  occupying  of  space  or 
the  presence  of  a  certain  quantity  of  volume  energy.  If,  for  instance, 
the  quantity  of  matter  be  compressed,  its  volume  is  diminished  and 
the  work  done  is  the  equivalent  of  this  compression.  Similarly  we 
speak  of  a  quantity  of  electricity  when  we  recognize  a  certain  num- 
ber of  definite  properties  in  a  given  place.  These  properties  are  not, 
however,  the  same  as  those  which  characterize  the  presence  of 
matter.  A  quantity  of  electricity  does  not  fill  space  or  possess  vol- 
ume energy,  and  hence  cannot  be  grasped  by  the  hand.1  The  ques- 

1  It  should  be  noted,  however,  that  Helmholtz  and  others  have  attributed  an 
atomic  structure  to  electricity,  assuming  the  existence  of  positive  and  negative 
elementary  particles.  According  to  this  view  we  must  assume  the  existence 
of  two  new,  uuivalent,  and  nearly  massless  elements,  namely,  positive  and  iu^::i- 
tive  electrons 


FORMS  OF   ENERGY  AND  THEIR  MEASUREMENT         27 

tion  then  often  arises :  What  is  the  nature  of  electricity  and  what  is 
meant  by  quantity  of  electricity  ?  The  question,  What  is  the  nature 
of  matter  ?  however,  is  but  seldom  raised.  The  two  questions  are 
equally  idle,  for  the  terms  matter  and  electricity  are  nothing  more 
than  expressions  or  collective  names  for  certain  groups  of  definite 
properties. 

Mechanical  work  may  be  transformed  into  electrical  energy  by 
rubbing  a  stick  of  sealing  wax  with  a  woolen  cloth.  In  this  case 
both  the  sealing  wax  and  the  cloth  become  electrified,  the  one  with 
positive,  and  the  other  with  negative  electricity.  It  is  a  well-known 
law  of  nature  that  whenever  electrical  energy  is  produced,  it  always 
appears  simultaneously  in  two  separate  places,  although  these  places 
may  lie  exceedingly  near  to  each  other. 

It  is  usual  to  speak  of  a  quantity  of  electricity,  Q,  as  passing 
through  a  circuit  in  the  direction  in  which  copper  particles  are  car- 
ried during  electrolysis,  and  we  too  have  followed  the  custom. 
According  to  the  conceptions  of  the  present,  however,  when  a  quan- 
tity of  positive  electricity  passes  in  one  direction  during  electrolysis,  a 
certain  quantity  of  negative  electricity  passes  in  the  opposite  direction. 
These  quantities  are  carried  on  the  positive  and  negative  ions,  respec- 
tively. While  the  quantities  of  the  two  kinds  of  electricity  flowing 
may  not  be  equal,  they  must  always  be  so  related  to  each  other  that 
in  all  parts  of  an  electrolytic  conductor  their  sum  shall  be  the  same. 
In  metallic  conduction  it  is  assumed  that  the  electricity  which  flows 
is  negative  (negative  electrons).  However,  since  positive  electricity 
flowing  in  one  direction  through  a  metallic  circuit  produces  the  same 
effects  as  an  equal  quantity  of  negative  electricity  would  produce  in 
flowing  in  the  opposite  direction,  we  are  justified  for  the  sake  of 
simplicity  in  speaking  of  the  whole  quantity  of  electricity  of  an 
electric  current  as  flowing  in  the  direction  of  the  migration  of  copper 
particles.  It  should,  however,  be  borne  in  mind  that  this  method  of 
expression  is  not  strictly  correct. 

Electrical  Measurements.  —  In  measurements  of  any  kind  it  is 
necessary  to  establish  a  zero  or  starting  point.  For  the  intensity 
factor  of  heat  energy,  the  temperature,  the  absolute  zero  is  taken  at 
273  degrees  below  the  centigrade  zero  (—  273°  t).  For  the  intensity 
factor  of  volume  energy,  the  pressure,  the  absolute  zero  is  taken 
as  the  pressure  existing  in  a  vacuum.  For  the  intensity  factor  of 
kinetic  energy,  the  velocity,  there  is  no  absolute  zero  point  known. 
Only  relative  velocities  can  be  measured.  For  all  ordinary  meas- 
urements the  velocity  of  the  earth  is  considered  to  be  zero,  and 
when,  for  instance,  a  body  is  said  to  possess  a  velocity  U,  it  is  really 


A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 


meant  that  this  is  the  difference  between  its  absolute  velocity  and 
the  absolute  velocity  of  the  earth.  Similarly,  in  the  case  of  the 
intensity  factor  of  electrical  energy,  the  potential,  there  is  no 
absolute  zero  point  upon  which  measurement  may  be  based.  As 
in  the  case  of  velocity,  an  arbitrary  zero  point  has  been  adopted. 
Accordingly,  zero  potential  is  taken  as  the  potential  which  exists  at 
the  surface  of  the  earth.  If  it  is  desired  to  bring  the  potential  of 
any  point  of  an  electric  circuit  to  the  potential  zero,  it  is  only 
necessary  to  connect  this  point  with  the  earth  by  a  good  conductor, 
and  thus,  in  a  way,  make  this  point  a  part  of  the  earth's  surface. 

Electrical  potentials  are  measured  by  means  of  electrometers,  of 
which  there  are  many  forms,  most  of  which  need  not  be  considered 
here.  The  principle  is  the  same  whatever  the  form  (excepting 
galvanic  electrometers),  and  may  be  understood  from  a  description 
of  one  of  the  simplest  forms,  known  as  the  gold-leaf  electrometer, 
shown  in  Figure  13. 

If  the  metal  rod  c  be  connected  with  the  earth,  the  strips  of  gold 
leaf  a  and  b  are  brought  to  zero  potential  and  hang  in  parallel  posi- 
tions. If  now,  after  disconnecting  the 
electrometer  from  the  earth,  it  be 
brought  into  contact  with  a  point  whose 
potential  is  to  be  measured,  positive  or 
negative  electricity  passes  from  this 
point  to  the  strips  of  gold  leaf,  which 
immediately  separate  as  shown  by  the 
dotted  line  in  the  figure.  This  is  due 
to  the  electrostatic  repulsion  of  the 
like  kinds  of  electricity  upon  them. 
The  greater  the  potential  at  the  point 
the  greater  the  quantity  of  electricity 
which  will  pass  to  the  gold  leaves  and 
the  farther  apart  they  will  separate. 
Consequently,  the  position  of  the  gold 
leaves  is  a  measure  of  the  potential  of 
the  point.  By  calibrating  the  elec- 
trometer, and  constructing  a  suitable 

scale,  unknown  potentials  may  be  measured  directly  in  volts  by 
means  of  it. 

There  remains  to  be  considered  a  peculiar  property  of  electrical 
energy,  namely,  the  additivity  of  the  intensity  factor,  the  potential. 
If  we  have  two  sources  of  such  energy,  as,  for  instance,  two  Daniel  1 
cells  having  the  same  electromotive  force,  1.10  volts,  and  connect 


FIG.  13 


FORMS  OF  ENERGY  AND  THEIR  MEASUREMENT 


29 


the  source  of  negative  electricity  of  each,  its  negative  pole,  with  the 
source  of  positive  electricity  of  the  other,  its  positive  pole,  the  result- 
ing combination  has  an  electromotive  force  equal  to  the  sum  of  the 
forces  of  the  two  cells,  or  2.20  volts.  If,  on  the  other  hand,  like 
poles  are  connected,  no  current  flows  through  the  circuit.  These  two 
combinations  are  represented  in  Figures  14  and  15. 


I 

; 

• 

—  w  — 

rv*— 

3 

~ 

=2=\= 

zlrfr 

"^~ 

-— 

f^Ei 

In 

CM 

2n 

Cu 

c 

luSQi 

Z,5C 

|| 

C 

hSQf 

ZnS\ 

\ 

FIG.  14 

A  very  different  relation  is  found,  for  instance,  in  the  case  of  the 
intensity  factor  of  heat  energy,  the  temperature.  It  is  not  possible 
in  a  similar  manner  to  add  two  temperatures.  If  we  have  two 
pieces  of  metal,  each  having  a  temperature  of  0°  at  one  end  and 
of  100°  at  the  other,  they  cannot  be  so  combined  as  to  produce  a 
temperature  of  200°. 


Cu 


Zn 


Zrcsa 


I 


Zn! 


FIG.  15 


With  electrical  energy,  when  a  potential-difference  exists  between 
two  points,  this  difference  is  not  altered  through  a  change  involving 
simply  an  increase  in  the  absolute  potential  of  those  points.  It  is 
because  of  this  fact  that  it  is  possible  to  produce  an  electromotive 
force  of  any  desired  magnitude.  If  the  negative  pole  of  a  Daniell 
cell  be  connected  with  the  earth,  at  the  positive  pole  there  is  a 
potential  of  +  1.10  volts.  If  now  to  this  positive  pole,  the  nega- 
tive pole  of  a  second  Daniell  cell  be  connected,  then  at  the  positive 


30  A   TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

pole  of  the  second  cell  there  will  be  a  potential  of  +  2.20  volts,  and 
so  on.  Cells  thus  connected  are  said  to  be  arranged  in  series  or  in 
tandem. 

Another  arrangement,  useful  for  certain  purposes,  consists  in  con- 
necting like  poles  of  different  cells  into  groups  and  then  connecting 
these  groups  with  each  other.  Although,  in  this  way,  no  increase  in 
electromotive  force  over  that  of  a  single  cell  is  obtained,  the  internal 
resistance  of  the  battery  thus  formed  is  less  than  that  of  the  single 
cell.  These  cells  are  said  to  be  arranged  in  parallel. 

Having  considered  the  fundamental  principles  relating  to  the 
electric  current,  we  may  now  turn  our  attention  to  the  subject  of 
electro-chemistry  itself.  As  an  introduction  to  this  branch  of  elec- 
trical science  the  history  of  electricity  is  briefly  presented  in  the 
following  chapter. 


CHAPTER   II 

DEVELOPMENT    OF    ELECTRO-CHEMISTRY    UP    TO    THE 
PRESENT    TIME 

Earliest  Records  of  Electrical  Phenomena. — A  little  more  than 
two  thousand  years  ago,  the  first  electrical  phenomena  of  which  we 
have  record  was  observed  by  Thales.  He  observed  that  under  cer- 
tain conditions  amber  (^Xc/crpoi/)  possessed  the  power  of  attracting 
light  bodies,  such  as  pieces  of  paper,  feathers,  etc.  Later,  it  was 
found  that  this  property  was  not  confined  to  amber  alone,  and  then 
it  became  known  as  "  ^AeKT/oov-like,"  which  later  was  contracted  to 
the  word  electrical.  The  phenomena  of  atmospheric  electricity, 
such  as  lightning,  St.  Elmo's  fire,  aurora  borealis,  etc.,  have  been 
known  from  the  earliest  times,  but  their  recognition  as  electrical 
phenomena  is  of  comparatively  recent  date. 

Up  to  the  beginning  of  the  seventeenth  century  our  knowledge  of 
electricity  was  extremely  scanty  and  imperfect.  At  that  time,  how- 
ever, it  was  somewhat  increased  by  the  work  of  William  Gilbert. 
He  showed  that  a  great  many  substances,  other  than  those  previously 
studied,  became  electrified  upon  being  rubbed,  but  that  none  of  the 
metals  possess  this  property.  He  was  the  first  to  declare  the  neces- 
sity of  rubbing  the  material  in  order  to  produce  electricity. 

From  this  time  on  an  increased  interest  was  taken  in  electrical 
phenomena,  resulting  in  the  discovery  of  means  for  the  production 
of  greater  electrical  effects  than  were  possible  through  the  rubbing  of 
such  substances  as  amber,  and  in  the  discovery,  by  Dufay,  in  1733, 
of  the  existence  of  two  opposite  kinds  of  electricity.  Dufay  called 
the  electricity  which  remains  on  the  glass,  vitreous,  and  that  which 
remains  on  the  resin,  resinous  electricity. 

At  the  end  of  the  eighteenth  century  five  different  sources  of 
electricity  were  known.  The  usual,  and  up  to  the  time  of  Franklin 
the  only,  source  of  electricity  was  friction.  Franklin  discovered 
that  the  atmosphere  was  a  second  source.  A  third  source  was  found 
by  Wilke,  who  observed  that  electricity  was  produced  when  fused 
substances  solidify.  This  he  named  "  electricitas  spontanea."  The 
warming  of  tourmaline  became  the  fourth  source.  The  fifth  and 

31 


32  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

last  source  was  found  in  the  living  animal  organism,  when  the  power 
of  certain  fish,  such  as  the  gymnotus,  torpedo,  and  silurus,  to  pro- 
duce electrical  shocks  was  recognized. 

The  Work  of  Galvani.  —  The  great  electrical  discovery  of  the 
eighteenth  century,  the  one  which  attracted  the  attention  of  the  best 
investigators  of  that  time,  and  which  has  proved  to  be  the  discovery 
of  a  much  more  productive  source  of  electricity  than  was  previously 
known,  we  owe  primarily  to  the  wife  of  Aloisius  Galvani,  Professor 
of  Medicine  in  the  University  of  Bologna.  She  observed  that  the 
freshly  prepared  hind  legs  of  a  frog  which  were  touching  a  scalpel, 
moved  as  if  alive  while  sparks  were  passing  from  an  electric  machine 
near  by.  She  called  Galvani's  attention  to  the  phenomenon,  and  in 
a  short  time  he  was  deeply  involved  in  a  study  of  it,  considering  it 
a  good  proof  of  his  pet  theory  that  the  animal  organism,  in  general, 
was  in  possession  of  electricity. 

In  carrying  on  his  experiments  he  was  accustomed  to  place  the 
preparations  of  frogs'  legs  upon  an  iron  railing  in  the  open  air.  He 
often  watched  the  contractions  taking  place  in  them  there,  and  con- 
ceived that  it  might  be  due  to  atmospheric  electricity.  He  observed, 
further,  that  when  lightning  was  discharged,  or  storm  clouds  ap- 
proached, contraction  in  the  frogs'  legs  was  most  often  produced. 

Repeating  this  experiment  during  a  series  of  calm,  clear  days,  and 
observing  no  effect  upon  the  frogs'  legs,  he  twisted  the  wire  which 
was  hooked  through  the  spine  of  the  frog  about  the  iron  railing 
from  which  the  preparation  was  hanging,  thinking  thus  more  easily 
to  discharge  any  atmospheric  electricity  which  might  have  accumu- 
lated in  the  preparation.  He  observed  muscular  contractions  which 
he  then  concluded  were  at  least  not  entirely  produced  by  atmos- 
pheric electricity.  Later  experiments  carried  on  in  a  room  showed 
him  conclusively  that  these  contractions  in  the  frog  preparations 
have  nothing  to  do  with  atmospheric  electricity,  and  that  they  can, 
under  certain  circumstances,  be  made  to  take  place  in  any  place 
at  any  time. 

The  breadth  of  influence  of  this  simple  discovery  is  almost  without 
parallel.  It  was  recognized  that  the  contractions  of  the  frogs'  legs 
were  produced  by  electricity.  The  question  then  arose  as  to  the 
source  of  this  electricity. 

Galvani  declared  that  the  electricity  existed  in  the  preparation, 
which  he  compared  to  a  Ley  den  jar.  The  muscles,  and  nerves, 
according  to  him,  correspond  to  the  two  coatings  of  the  Leyden  jar, 
and  the  wire  to  the  discharging  rod.  He  believed,  further,  that 
every  animal  organism  was  a  source  of  electricity,  to  a  greater  or 


DEVELOPMENT  OF  ELECTRO-CHEMISTRY  33 

less  degree,  as  in  the  case  of  the  electric  eel  and  certain  other  fishes, 
and  he  hoped  through  this  discovery  to  be  able  to  penetrate  further 
into  the  mysteries  of  life  itself. 

The  Work  of  Volta.  The  Voltaic  Pile.  —  For  a  time,  Galvani's 
opinions  were  very  generally  accepted  by  physicists,  many  of  whom 
had  repeated  the  above-mentioned  experiments.  Even  Volta,  who 
was  a  professor  in  the  University  of  Pavia,  and  who  already  had 
achieved  marked  distinction,  at  first  was  inclined  to  accept  these 
views.  Later,  however,  he  observed  that  the  effects  produced  were 
very  marked  when  the  back  of  the  frog  or  the  nerve  was  connected 
with  the  leg,  or  muscle,  by  a  wire  the  ends  of  which  were  of  dif- 
ferent metals,  while  the  effect  was  very  weak  or  entirely  wanting, 
when  a  wire  of  a  single  metal  was  used.  Upon  further  investigation 
he  found  that  whenever  two  metals  and  a  liquid  are  combined  to  make 
a  circuit,  an  electric  current  is  produced.  This  showed  clearly  that 
the  explanation  given  by  Galvani  was  untenable. 

From  these  experiments  Volta  concluded  that  the  source  of  the 
electricity  was  either  at  the  point  of  contact  of  the  two  different 
metals  of  the  circuit,  or  at  the  point  of  contact  of  the  two  metals 
with  the  liquid.  In  the  case  of  Galvani's  experiments  this  liquid 
was  the  moisture  of  the  preparation.  Volta  considered  the  frog's 
legs,  themselves,  to  be  nothing  more  than  a  delicate  electroscope, 
indicating  the  presence  of  an  electric  current  in  the  circuit.  He 
finally  concluded  that  the  principal  source  of  the  electricity  was  at 
the  point  of  contact  of  the  two  metals,  and  not  at  the  points  of  con- 
tact of  metal  and  liquid.  This  conclusion  has  been  commonly 
accepted  until  within  very  recent  years. 

As  a  sequence  of  his  experiments,  it  should  be  mentioned  that 
Volta  distinguished,  for  the  first  time,  between  two  classes  of 
electrical  conductors.  In  the  first  class,  he  included  the  metals, 
carbon,  and  certain  other  good  conducting  substances,  such  as  the 
metallic  sulfides ;  and  in  the  second  class,  all  conducting  solutions. 
This  distinction  is,  in  the  main,  still  recognized.  According  to  the 
prevailing  ideas  of  the  present  time,  conductors  of  the  first  class 
may  be  defined  to  be  such  as  conduct  the  electric  current  without  a 
movement  of  ponderable  matter,  and  conductors  of  the  second  class, 
such  as  conduct  the  electric  current  only  by  means  of  a  movement  of 
ponderable  matter.  The  effect  of  temperature  upon  the  two  classes 
of  conductors  is  remarkable,  in  that  in  general,  those  of  the  first 
class  conduct  electricity  less  readily,  and  those  of  the  second  class 
more  readily,  with  increasing  temperature.  It  has  also  been  found 
to  be  a  fact,  which  is  in  agreement  with  the  electro-magnetic  theory 


34  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

of  light,  that  metallic  conductors  are,  even  in  very  thin  layers, 
opaque,  while  other  conductors  in  thin  layers  are  always  more  or  less 
transparent  to  ordinary  light.  This  behavior  towards  heat  and 
light  is  a  convenient  means  of  distinguishing  between  the  two  classes 
of  conductors  in  such  doubtful  cases  as  are  met  among  the  oxides. 

For  conductors  of  the  first  class,  Volta  soon  established  the  con- 
tact electromotive  series,  which  is  a  table  of  conductors  so  arranged 
that  if  any  two  of  them  be  connected  with  each  other  and  also  with 
a  conductor  of  the  second  class  (a  liquid  thus  completing  a  circuit) 
an  electric  current  will  flow  from  the  conductor  higher  in  the  table 
or  series  through  the  liquid  to  the  other.  Moreover,  the  current  is 
greater,  the  farther  apart  the  two  chosen  metals  stand  in  the  series. 

[In  the  following  table  is  given  such  a  contact-series :  — 

ZINC 

LEAD 

TIN 

IRON 

COPPER 

PLATINUM] 

After  the  establishment  of  the  order  of  contact  electromotive 
forces,  Eitter  made  the  discovery,  entirely  unappreciated  at  the 
time,  that  this  order  is  the  same  as  the  order  in  which  metals  pre- 
cipitate one  another  from  solutions  of  their  salts.  A  reference  to 
the  above  contact-series  will  make  this  clearer.  Metallic  zinc  when 
placed  in  a  solution  of  a  lead  salt  dissolves  and  causes  the  separation 
from  the  solution  of  metallic  lead.  Similarly,  metallic  lead  causes 
the  separation  of  metallic  tin,  and  so  on  down  the  series.  Moreover, 
any  metal  causes  the  separation  of  all  the  other  metals  of  the  series 
which  are  situated  below  it,  from  solutions  of  their  salts.  The 
identity  of  the  order  of  the  contact  electromotive  forces  of  the  metals  and 
the  order  of  their  precipitating  powers  shows  a  relation  between  electricity 
and  chemistry.  The  discovery  of  this  relation  may  be  considered  to 
mark  the  beginning  of  scientific  electro-chemistry. 

A  little  later,  Volta  stated  his  Law  of  Contact  Electromotive  Force. 
This  law  states  that  the  same  potential  always  exists  between  two 
given  metals,  whether  they  are  in  contact  with  each  other  directly, 
or  only  through  a  series  of  other  metals.  [The  following  table  gives 
the  metals  in  the  order  of  the  contact  electromotive  force  series, 
together  with  the  potential-difference  between  adjacent  metals :  — 


DEVELOPMENT  OF  ELECTRO-CHEMISTRY  35 

METALS  POTENTIAL-DIFFBBBNCM 

IN  VOLTS 
Zinc 

0.210 

Lead 

0.069 

Tin 

.        .        .    0.313 

Iron 

0.146 

Copper 

0.238 

Platinum  0.976 

According  to  the  above  law,  whether  zinc  be  connected  with  plati- 
num directly  or  through  the  series  of  metals,  lead,  tin,  iron,  copper, 
etc.,  the  difference  of  potential  between  them  will  be  0.976  volt.]  It 
also  follows  from  the  above  law,  that  it  is  impossible  to  obtain  an 
electric  current  from  a  circuit  made  up  entirely  of  metals ;  for  in 
such  a  circuit-  the  sum  of  all  the  potential-differences  is  equal  to 
zero.  [This  is  at  once  evident  from  the  following  diagram  :  — 


021 

CT»N  •  LEAD =S±—  ZINC • 

J 
0146  O238 

IRON  •  COPPER-     *T"    PLATINUM* 

FIG.  16 

The  sum  of  the  potential-differences  at  the  points  of  contact  of  dis- 
similar metals  urging  an  electric  current  in  one  direction  (0.21  + 
.069  +  0.313  +  0.146  +  0.238)  is  exactly  equal  to  the  potential-differ- 
ence (0.976)  urging  an  electric  current  in  the  opposite  direction.] 

The  law  of  contact  electromotive  force,  according  to  Volta,  does 
not  apply  to  conductors  of  the  second  class.  Since  he  believed  that 
only  slight  potential-differences  were  produced  at  the  points  of  con- 
tact of  the  metals  with  the  conducting  liquid,  he  reasoned  that  the 
two  metals  could  be  connected  with  a  liquid  with  scarcely  any 
change  in  potential  from  one  metal  to  the  other  through  the  liquid. 
[Accordingly,  if  the  circuit  shown  in  Fig.  16  be  broken,  at  a,  and  the 
two  ends  dipped  in  a  conducting  liquid,  a  current  would  flow  through 
the  circuit  so  produced  under  a  potential-difference  of  nearly  0.976 
volt.] 

As  long  as  investigators  were  mainly  devoted  to  the  study  of  fric- 
tional  electricity,  scarcely  any  attention  was  given  to  the  relations 


36 


A   TEXT-BOOK  OF   ELECTRO-CHEMISTRY 


between  electrical  and  chemical  processes.  This  was  in  a  large  de- 
gree due  to  the  fact  that  the  quantities  of  electricity  which  were 
produced  by  the  friction  method  were  too  small  to  bring  about  any 
considerable  chemical  effects.  A  few  facts  bearing  upon  the  rela- 
tion between  these  two  energy  forms  were  known  as  early  as  the 
middle  of  the  eighteenth  century.  It  was  known  that,  by  means  of 
electric  sparks,  metals  could  be  "  revived "  or  obtained  from  their 
oxides ;  that  air,  other  gases,  and  water  were  affected  by  the  passage 
of  electric  sparks  had  also  been  observed.  The  chemical  effect  of 
the  electric  current  was  first  studied  on  a  large  scale  after  Volta  had 
constructed  the  apparatus  commonly  known  as  the  Voltaic  pile.  [A 
diagram  of  this  apparatus  is  shown  in  Fig.  17.] 

It  consists  of  pairs  of  plates  of  dissimilar  metals,  as,  for  instance, 
silver  and  zinc,  separated  from  each  other  by  pieces  of  absorbent 

material  like  blotting  paper  or 
flannel  cloth,  moistened  with  a 
liquid  conductor  such  as  a  salt 
solution.  The  strength  of  the 
pile  depends  upon  the  metals 
chosen,  and  upon  the  number  of 


fa 


Afl 


Zn 


Zn 


3 


tu 


Pj>fl  metallic  pairs  used  in  its  con- 
Lyyfif  structi on.  [Referring  to  Fig. 
17,  the  greatest  potential-differ- 
ence is  obtained  between  the 
poles  a  and  6,  decreasing  as, 
instead  of  the  pole  a,  the  poles 
a',  a",  etc.,  are  taken.]  At  the 
beginning  of  the  present  cen- 
tury almost  every  one  who  was 
in  a  position  to  do  so  built  a 
Voltaic  pile,  and  consequently  the  scientific  papers  of  that  period 
were  filled  with  descriptions  of  experiments  in  which  the  pile  was 
used. 

The  Electrolytic  Decomposition  of  Water.  —  It  is  worthy  of  notice 
that  Volta  himself  says  nothing  of  the  chemical  actions  which  may 
be  produced  with  his  apparatus,  although  it  is  evident  from  his  ex- 
periments that  he  must  have  observed  the  electrical  decomposition 
of  water.  This  indicates  that  he  did  not  appreciate  the  significance 
of  this  phenomenon.  The  discovery  that  water  could  be  decom- 
posed by  means  of  the  Voltaic  pile  thus  became  the  work  of  others. 

In  the  year  1800  Nicholson  and  Carlisle  showed  that  on  conduct- 
ing an  electric  current  through  water,  by  dipping  the  two  terminals 


DEVELOPMENT  OF  ELECTRO-CHEMISTRY 


37 


of  a  voltaic  pile  into  it,  at  one  of  the  terminals  hydrogen,  and  at 
the  other  oxygen,  was  produced.  The  fact  was  also  not  overlooked 
that  the  water  about  the  terminal  at  which  hydrogen  was  produced 
became  alkaline,  and  that  about  the  other  terminal  became  acid. 

Measurement  of  the  Potentials  of  a  Voltaic  Pile. —  It  is  surprising 
that,  as  early  as  1802,  thorough  measurements  of  potentials  of  the 
Voltaic  pile,  which  are  still  accepted  as  correct,  were  made  by  Er- 
mann.  Some  of  the  results  have  already  been  considered  in  the 
introduction,  and  others  will  now  be  considered. 

Ermann  inserted  a  silver  tube,  filled  with  water,  into  the  circuit. 
The  ends  of  the  tube  were  closed  with  pieces  of  glass  through  which 
the  terminal  wires  of  a  battery  were  passed,  making  contact  with 
the  water  inside  of  the  tube.  By  connecting  an  electroscope  to  any 
desired  point  of  the  silver  tube,  the  presence  of  electricity  through- 
out the  tube  was  shown. 

Ermann  also  established  the  important  fact  that  the  column  of 
water  between  the  two  ends  of  the  battery  terminal  wires  actually 
contains  electricity  during  the  galvanic  action.  The  fall  in  potential 
when  the  column  of  liquid  forms  a  part  of  the  circuit  still  takes 
place  according  to  the  principles  discussed  on  pages  11  to  13.  In 
this  case,  a  sudden  fall  in  potential  takes  place  at  the  poles  due  to 
the  work  performed  there. 

When  wires  are  placed  between  the  two  ends  of  the  battery  wires 
in  the  tube  as  shown  in  Figure  18,  Ermann  observed  that  gas  was 
evolved  at  each  wire  end ;  and  that  in  every  case  an  end  at  which 
hydrogen  appeared  was  adjacent  to  one  at  which  oxygen  appeared. 
This  is  indicated  in  Figure  18. 


H,  0,       HB  Q,      H,  Q,      Ha  0,      H*  0* 


FIG.  18 

The  electric  current  was  conducted  partly  by  the  water  and  partly  by 
the  wires.1  In  this  case  also,  the  fall  of  electroscopic  potential  took 
place  as  in  the  cases  already  considered. 

1  If  the  water  has  become  good-conducting  by  dissolving  oxygen  salts,  or  if 
the  platinum  wire  is  too  short,  no  evolution  of  gas  takes  place  at  the  ends  of  the 
wire,  and  the  wire  takes  no  part  in  the  conduction  of  the  electric  current.  The 
evolution  of  gas  and  the  conduction  of  the  electric  current  by  th^wjre^ta^es, 
place  appreciably  only  when  thenpQtsn&^^y^tf^ 


38  A  TEXT-BOOK  OF   ELECTRO-CHEMISTRY 

By  connecting  the  circuit  with  the  earth,  it  is  possible  to  have 
either  positive  or  negative  electricity  alone  in  the  column  of  water 
and  the  wires.  It  is  also  possible  to  cause  one  part  of  the  circuit  to 
exhibit  positive,  while  the  rest  exhibits  negative,  electricity. 

The  Migration  of  Acid  and  Alkali,  and  the  Discovery  of  the  Alkali 
Metals.  —  It  was  very  difficult  for  the  early  investigators  to  compre- 
hend the  formation  of  hydrogen  and  alkali  at  one  of  the  points  where 
the  wires  from  a  Voltaic  pile  came  into  contact  with  water,  and  of 
oxygen  and  acid  at  the  other.  It  was  a  question  with  them  whether 
or  not  the  acid  and  alkali  were  actually  created  by  the  action  of  elec- 
tricity on  water.  Such  a  question  was  not  absurd,  for  at  that  time, 
the  law  of  the  conservation  of  matter  was  not  at  all  generally  recog- 
nized, It  was  one  which  required  an  experimental  answer.  The 
task  of  answering  this  question  was  undertaken  first  by  Simon,  and 
then  a  few  years  later  by  Davy,  who  showed,  by  a  series  of  very  care- 
ful experiments,  that  pure  water  is  decomposed  into  hydrogen  and 
oxygen  by  the  electric  current,  without  the  formation  of  acid  and 
alkali,  and  that  the  formation  of  the  latter,  in  earlier  experiments, 
was  due  to  the  presence  of  impurities  in  the  water.  He  performed, 
furthermore,  experiments  of  the  greatest  importance  upon  the  migra- 
tion of  acids  and  bases  to  the  two  poles,  respectively,  for  which  a 
satisfactory  explanation  was  not  found  until  the  establishment  of  the 
accepted  theories  of  the  present  time.  This  experiment  is  briefly 
described  at  this  point  because  the  phenomena  involved  should  be 
known.  It  will  be  more  thoroughly  understood  after  the  modern 
theories  have  been  studied.  The  reader  is  advised  then  to  attempt 
to  discover  the  explanation  of  this  experiment,  as  thereby  he  will 
recognize  more  fully  the  advantages  of  modern  conceptions. 

If  two  platinum  wires  are  connected  to  the  poles  of  a  voltaic  pile, 
and  the  free  end  of  one  of  them  is  placed  in  a  vessel  filled  with  pure 
water,  and  the  free  end  of  the  other  in  one  containing  a  solution  of 

wire  and  of  the  liquid  layer  parallel  to  the  wire  reaches  about  the  value  1.7  volts 
(the  decomposition  voltage  of  water).  This  process,  which  is  of  great  industrial 
importance,  cannot  be  completely  understood  until  the  study  of  polarization 
(Chapter  VIII)  is  taken  up.  For  a  further  discussion  see  Danneel,  Ztschr. 
fflektrochem.,  9,  256  (1903). 

When  higher  current  densities  are  used,  the  fractional  part  of  the  current 
which  flows  through  the  wire  becomes  greater  and  greater.  This  fact  has  recently 
received  a  practical  application  in  the  fusion  of  metals  under  water  by  means  of 
large  currents  of  electricity.  The  water  is  heated  but  slightly  by  the  electric 
current  because  only  a  very  small  part  of  the  current  passes  through  it.  More- 
over the  heating  of  the  water  by  the  glowing  rnetal  is  reduced  to  a  minimum  by 
the  existence  of  the  Leidenfrost's  phenomenon. 


DEVELOPMENT  OF  ELECTRO-CHEMISTRY 


39 


potassium  sulfate,  the  two  vessels  being  connected  by  means  of  a  tube 
filled  with  water  as  shown  in  Figure  19,  acid  is  formed  at  the  wire 
which  is  connected  with  the  positive  pole  of  the  pile  and  alkali  is 
formed  at  the  other  wire. 

The  same  result  is  obtained  if  three  vessels,  connected  in  this 
manner,  and  filled,  respectively,  with  water,  potassium  sulfate  solu- 
tion, and  water  are  used 
with  the  two  platinum 
electrodes  dipping  into  the 
end  vessels.  The  positive 
pole  appears  to  possess  an 
attraction  for  the  acid,  and 
the  negative  pole  for  the 

base,  resulting  in  the  de-  FlG  19 

composition  of  the  salt. 

Davy  desired  to  study  the  motion  of  the  acid  and  base  towards  the 
positive  and  negative  poles,  respectively.  He  proposed  to  follow  this 
motion  by  means  of  litmus  paper,  and  found  to  his  astonishment,  that 
the  first  appearance  of  acid  or  alkali  was  not  in  the  water  at  the  point 
where  it  came  into  contact  with  the  salt  solution,  but  at  the  elec- 
trodes, whence  it  gradually  diffused  throughout  the  water.  If  acid 
and  alkali  could  thus  be  made  to  pass  through  pure  water  in  going 
to  the  poles,  without  affecting  the  litmus  on  the  way,  Davy  ques- 
tioned whether  it  was  not  also  possible  that  they  might  pass  through 
substances  for  which  they  had  a  great  chemical  affinity  without  acting 
upon  them.  He  found  that  an  interposed  concentrated  acid  solution 
did  not  in  any  way  hinder  the  passage  of  alkali  to  its  pole,  nor  did  a 
concentrated  alkali  solution  hinder  the  passage  of  acid.  There  was 
found,  however,  in  the  interposed  acid  and  alkali  solutions  some  of 
the  corresponding  salt.  This  seemed  to  indicate  that  the  chemical 
affinity  had  caused  some  of  the  passing  compound  to  be  retained. 
If,  further,  barium  chloride  be  used  to  intercept  the  passage  of  sul- 
furic  acid,  barium  sulfate  is  formed,  and  only  after  a  long  time 
does  sulfuric  acid  reach  its  pole.  Here,  thought  Davy,  the  chemical 
affinity  has  completely  overcome  the  electrical  attraction. 

A  little  later  Davy  crowned  his  experimental  work  with  the  dis- 
covery of  the  alkali  metals  by  the  separation  of  them  from  their  fused 
hydrates  by  means  of  the  electric  current.  He  thus  laid  the  founda- 
tion for  the  present  day  commercial  preparation  of  metallic  sodium, 
as,  for  instance,  by  the  so-called  Castner  process. 

This  process  consists,  principally,  in  passing  an  electric  current 
through  sodium  hydrate  which  has  been  heated  but  slightly  above  its 


40  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

point  of  fusion.  The  metallic  sodium  which  separates  at  the  cathode 
is  kept  from  moving  away  toward  the  anode  by  means  of  a  gauze  of 
iron  wire  of  fine  mesh.  At  the  anode  both  oxygen  and  water  are 
formed.  The  former  is  evolved  from  the  fusion  to  a  great  extent, 
while  the  latter  dissolves  in  the  fusion  and  finally  reaches  and  reacts 
with  the  metallic  sodium  at  the  cathode,  forming  there  hydrogen 
and  sodium  hydroxide.  In  this  way  one  half  of  the  metallic  sodium 
set  free  by  the  current  is  reconverted  into  the  hydroxide,  so  that  the 
yield  of  sodium  by  this  method  never  exceeds  fifty  per  cent.  If 
the  temperature  is  too  high,  the  metallic  sodium  also  dissolves  in  the 
fusion  and  becomes  oxidized  at  the  anode.  The  yield  of  metallic 
sodium  finally  becomes  zero.1  The  following  equations  represent  the 
process  under  normal  conditions.  By  the  action  of  the  electric  cur- 
rent, 


at  the  cathode, 

2Na  +  2H20  =  2NaOH  +  H2;  and 

at  the  anode, 

40H=02  +  2H20. 

The  Rise  and  Fall  of  the  Electro-chemical  Theory  of  Berzelius.  —  At 
the  time  of  Davy's  great  work,  Berzelius  was  just  beginning  his  scien- 
tific investigations.  In  one  of  the  first  of  these,  carried  out  jointly 
with  Hisinger,  he  studied  the  action  of  the  electric  current  upon  solu- 
tions of  various  inorganic  substances,  resulting  chiefly  in  the  estab- 
lishment of  the  first  electro-chemical  theory.  This  theory  dominated 
the  science  of  chemistry  for  many  decades.  According  to  it,  each 
chemical  atom,  when  in  contact  with  another,  possesses,  like  a  magnet, 
an  electro-positive  and  an  electro-negative  pole.  Moreover,  one  of 
these  poles  is  usually  much  stronger  than  the  other.  Consequently 
an  atom  behaves  as  if  it  possessed  but  one  pole,  either  electro-positive 
or  electro-negative  according  as  the  positive  or  negative  pole,  respec- 
tively, predominates  in  strength.  The  magnitude  and  sign  of  this 
resultant  polarity  upon  the  atoms  of  a  given  element  determines  its 
chemical  behavior.  If,  for  instance,  the  atoms  of  an  element  are 
electro-positive,  it  will  react  with  elements  whose  atoms  are  electro- 
negative, and  conversely.  During  this  reaction,  the  two  kinds  of 
electricities  neutralize  each  other  more  or  less  completely,  according 
to  the  degree  of  inequality  existing  between  the  positive  and  nega- 

1  For  a  further  discussion  see  the  article  by  Leblanc  and  Erode,  "The  Elec- 
trolysis of  Fused  Sodium  and  Potassium  Hydroxides,"  Ztschr.  Elektrochem., 
tfud  Lstesil  xisad  8&d  iloirlw  staled  inuiJooa 


DEVELOPMENT   OF  ELECTRO-CHEMISTRY  41 

tive  charges  upon  the  reacting  atoms.  If  complete  neutralization 
does  not  take  place,  the  resulting  compound  itself  is  electro-positive 
or  electro-negative  according  as  the  electro-positive  are  greater  or 
less  than  the  electro-negative  charges  upon  the  component  atoms. 
Compounds  which  thus  possess  a  resultant  polarity  may  then  enter 
into  further  combinations  with  each  other  in  such  a  way  as  to 
form  a  complex  compound  which  is  more  nearly,  or  quite,  neutral. 
Thus  the  theory  explains  not  only  the  formation  of  simple  com- 
pounds from  their  elements,  but  also  the  formation  of  complex  com- 
pounds, such  as  double  salts,  from  their  component  simple  compounds. 

The  essential  elements  of  the  electro-chemical  theory  may,  perhaps, 
be  more  easily  comprehended  from  a  consideration  of  a  concrete 
example.  Adopting  the  table  of  atomic  weights  used  at  that  time, 
the  oxide  of  potassium  would  be  represented  by  the  symbol  KO. 
According  to  the  electro-chemical  theory,  the  charge  of  positive  elec- 
tricity on  the  potassium  atom  is  greater  than  that  of  negative  elec- 
tricity on  the  oxygen  atom,  and,  consequently,  the  compound  KO 
still  possesses  a  certain  excess  charge  of  positive  electricity.  Sulfur 
combines  with  oxygen,  forming  the  compound  S03.  In  this  case  a 
negative  sulfur  atom  combines  with  three  negative  oxygen  atoms, 
forming  the  negative  compound  S03.  Berzelius  explained  the  ener- 
getic action  between  these  two  negative  substances,  by  assuming 
that  the  sulfur  atoms  possess  a  comparatively  great  positive  charge 
as  well  as  the  predominating  negative  charge,  and  that  the  negative 
charge  of  the  oxygen  neutralizes  the  former.  Since  the  molecules 
of  potassium  oxide  are  positively  charged  and  those  of  sulfur  trioxide 
negatively  charged,  these  two  kinds  of  molecules  may  combine 
chemically  with  a  partial  or  complete  neutralization  of  their  charges, 
forming  KO  •  S03.  It  was  supposed  that  the  latter  compound  still 
retained  a  slight  positive  charge.  An  entirely  similar  explanation 
applies  to  the  formation  of  aluminium  sulfate,  A1203  •  (S03)3,  ex- 
cept that  it  was  supposed  that  this  salt  retains  a  slight  negative 
charge.  Assuming  the  sulfates  of  potassium  and  aluminium  to  be 
thus  oppositely  charged,  it  follows  from  the  theory  that  it  should  be 
possible  to  cause  them  to  combine  with  each  other.  This  explains 
the  formation  of  the  double  salt,  KO  •  S08  —  A1203  -  (S03)3. 

According  to  the  above  theory,  chemical  and  electrical  processes 
are  closely  related,  and  all  compounds  have  a  dualistic  nature,  being 
formed  of  an  electro-positive  and  an  electro-negative  component. 
This  theory  is  therefore  known  as  the  electro-chemical  or  dualistic 
theory.  It  was  applied  throughout  the  domain  of  inorganic  chemis- 
try, 


42  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

and  although  it  contained  many  arbitrary  assumptions,  it  performed 
a  great  service  to  science  because  of  its  systematizing  influence. 

The  Laws  of  Electro-chemical  Change.  —  For  several  decades  after 
the  establishment  of  the  dualistic  theory,  no  considerable  advance 
was  made  in  electro-chemistry.  This  lack  of  progress  was  soon 
counterbalanced  by  the  important  discoveries  which  were  made  by 
Faraday  about  the  year  1835.  He  was  the  first  to  show  that,  whether 
electricity  is  produced  by  means  of  friction  or  by  means  of  a  voltaic 
pile,  it  is  capable  of  producing  the  same  effects.  This  fact  convinced 
him  that  there  exists  but  one  kind  of  positive  and  one  of  negative 
electricity.  He  next  attempted  to  discover  a  relation  between  the 
quantity  of  electricity  flowing  through  a  circuit  and  the  magnitude 
of  the  chemical  and  magnetic  effects  which  it  could  produce.  His 
results  may  be  expressed  as  follows :  — 

The  magnitude  of  the  chemical  and  of  the  magnetic  effects  produced 
in  a  circuit  by  an  electric  current  is  proportional  to  the  quantity  of 
electricity  which  passes  through  the  circuit. 

A  further  discovery  was  made  by  Faraday  by  comparing  the 
quantities  of  different  substances  in  solution  which  are  decomposed 
by  the  same  quantity  of  electricity.  This  comparison  may  be  made 
in  a  very  simple  manner  by  connecting  into  one  circuit  a  series  of 
solutions  of  different  substances  so  that  the  same  quantity  of  elec- 
tricity passes  through  each  solution.  The  chemical  decomposition 
produced  by  the  electric  current  in  each  solution  may  then  be  deter- 
mined by  analysis.  The  results  obtained  may  be  summarized  as 
follows :  — 

The  quantities  of  the  different  substances  which  separate  at  the  elec- 
trodes throughout  the  circuit  are  directly  proportional  to  their  equivalent 
weights,  and  are  independent  of  the  concentration  and  the  temperature 
of  the  solutions,  the  size  of  the  electrodes,  and  all  other  circum- 
stances. 

The  above  statement,  expressing  the  relation  between  the  quantity 
of  electricity  flowing  through  a  conductor  of  the  second  class  and 
the  quantity  of  chemical  decomposition  which  is  produced  by  it,  is 
known  as  the  law  of  electro-chemical  change,  or  Faraday's  law. 

If  a  solution  of  an  acid,  of  a  mercurous  salt,  and  of  a  mercuric 
salt  be  connected  into  a  circuit  by  means  of  platinum  electrodes,  and 
the  chemical  decomposition  at  the  negative  electrode  be  measured 
in  each  case,  it  is  found  that  for  every  gram  of  hydrogen  liberated 
in  the  first  solution,  two  hundred  grams  of  mercury  are  set  free  in 
the  second,  and  one  hundred  grams  in  the  third.  These  quantities 
are  identical  with  the  equivalent  weights  of  these  elements.  The 


DEVELOPMENT  OF  ELECTRO-CHEMISTRY  43 

quantities  of  mercury  separated  are  to  each  other  as  2  :  1,  or  inversely 
proportional  to  the  valences  of  mercury  in  the  two  solutions. 

The  fact  just  illustrated,  that  the  quantity  of  an  element  deposited 
by  a-  given  quantity  of  electricity  increases  the  lower  its  valence  in 
the  solution  used,  is  of  commercial  importance.  For  instance,  the 
same  quantity  of  electricity  deposits  twice  as  much  copper  from  a 
cuprous  chloride  (in  a  sodium  chloride  solution)  as  from  a  cupric 
chloride  solution.  Therefore,  in  obtaining  copper  by  the  electrolytic 
process,  the  former  solution  is  preferred  if  other  circumstances  permit. 

The  above  laws  discovered  by  Faraday,  both  that  relating  to  the 
proportionality  between  the  quantity  of  electricity  and  the  quantity 
of  chemical  change  which  it  may  produce,  and  that  relating  to  the 
deposition  of  equivalent  weights  of  different  substances  by  the  same 
quantity  of  electricity,  have  been  proven  to  hold  with  great  exact- 
ness. At  the  present  time,  there  is  no  reason  for  doubting  their 
validity  in  any  case.  They  hold  not  only  for  all  solvents,  but  for 
fusions  as  well. 

The  quantity  of  electricity  which,  according  to  most  recent  meas- 
urements, is  necessary  to  deposit  exactly  one  equivalent  weight  of 
any  conducting  substance  is  equal  to  96,540  coulombs.1  This  num- 
ber, which  will  be  denoted  by  Q,  represents  the  electro-chemical  unit 
of  electricity,  and  is  called  the  electro-chemical  constant.  The  quan- 
tity of  electricity,  Q,  will  then  decompose  169.97  grams  of  silver 
nitrate  with  the  deposition  on  the  negative  pole  of  107.93  grams  of 
metallic  silver.  It  follows  from  these  values  that  the  quantity  of 
silver  deposited  by  one  coulomb  of  electricity,  or  in  other  words  by 
a  one-ampere  current  in  one  second,  is  equal  to 


It  is  evident  from  these  figures  that  in  the  case  of  conductors  of  the 
second  class,  large  quantities  of  electricity  move  with  very  small  quan- 
tities of  matter.  In  this  connection  it  is  interesting  to  note  that, 
while  one  hundred  coulombs  of  electricity  deposit  but  0.111  gram 
of  silver,  or  but  a  little  more  than  0.001  gram  of  hydrogen,  it  is 
sufficient  to  charge  the  earth's  surface  to  a  potential  of  more  than 
100,000  volts. 

1  This  value  is  that  adopted  by  the  International  Congress  for  Applied  Chem- 
istry held  in  1903.     It  will  be  used  throughout  the  book.     According  to  the 
measurements  of  Richards  and  Heimrod  (Ztschr.  phys.  Chem.,  41,  302,  1902), 
the  value  of  this  constant  is  96,580  coulombs. 

2  The  table  at  the  end  of  the  book  contains  the  values  for  many  other 
metals,  etc. 


44  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

The  law  of  electro-chemical  change,  when  first  published  by  Fara- 
day, met  with  great  opposition,  due  principally  to  the  imperfect 
conception  at  that  time  of  the  fundamental  principles  relating  to 
electrical  energy  and  to  faulty  understanding  of  the  law.  Even 
Faraday  himself  did  not  have  a  clear  idea  of  them.  The  quantity 
of  electricity,  for  instance,  was  not  distinguished  from  the  quantity 
of  electrical  energy.  Now  the  law  refers  to  quantity  of  electricity, 
but  not  at  all  to  quantity  of  electrical  energy;  for  it  states  that 
when  a  given  quantity  of  electricity  passes  through  any  solution,  it 
always  produces  the  decomposition  of  the  same  number  of  chemical 
equivalents  of  the  solute  or  solutes.  It  states  nothing  in  regard  to 
the  quantity  of  electrical  energy  necessary  to  effect  this  decomposition. 
Among  those  who  did  not  understand  correctly  the  meaning  of  the 
law  was  Berzelius.  He  understood  the  law  to  state  that  equal  quan- 
tities of  energy  were  required  to  effect  the  decomposition  of  equal 
chemical  equivalents  of  different  substances.  This  made  the  law 
seem  absurd,  for  the  chemical  affinity  or  cohesion  between  the 
particles  separated  by  the  electric  current  in  the  case  of  substances 
differing  widely  from  one  another  cannot  be  the  same.  The  factors 
of  an  energy  are  still  often  mistaken  for  the  energy  itself. 

Electro-chemical  Nomenclature.  —  Besides  discovering  the  law  of 
electro-chemical  change,  Faraday  also  devised  the  system  of  electro- 
chemical nomenclature.  To  explain  the  phenomena  observed  during 
the  passage  of  electricity  through  a  solution,  he  assumed  that  the 
movement  of  electricity  was  associated  with  a  movement  of  particle© 
of  ponderable  matter.  These  particles  he  called  ions.  Those  ions 
which  move  in  the  direction  of  the  positive  electricity  he  called 
cations,  and  those  which  move  in  the  opposite  direction,  anions. 
Substances  which  conduct  electricity  with  an  associated  movement 
of  ions,  or  conductors  of  the  second  class,  Faraday  called  electrolytes, 
and  to  the  conduction  of  electricity  by  an  electrolyte  he  gave  the 
name  electrolysis.  The  name  electrode  he  gave  to  the  surface  of  con- 
tact between  conductors  of  the  first  and  second  classes  of  the  circuit 
That  surface  to  which  the  cations  move  received  the  name  cathode 
and  that  to  which  the  anions  move,  the  name  anode.  These  terms 
will  be  used  throughout  the  remainder  of  the  book. 

Development  of  the  Present  Theory  of  Electrolysis.  The  Grotthus 
Theory.  —  Those  who  first  recognized  the  decomposition  of  water  by 
an  electric  current,  as  already  indicated,  sought  an  explanation  for 
the  simultaneous  appearance  of  hydrogen  at  one  electrode  and  of 
oxygen  at  the  other.  It  was  not  until  1805,  however,  that  a  com- 
prehensive theory  for  thijTplienomenoh  was"pu!f ToYwardV  "During 


DEVELOPMENT  OF  ELECTRO-CHEMISTRY 


45 


that  year  such  a  theory  was  published  by  Grotthus.  According  to 
this  theory,  the  electric  current  charges  one  electrode  positively  and 
the  other  negatively,  and  these  charged  electrodes  then  exert  an 
electrical  influence  upon  the  water  molecules.  Under  this  influence 
the  water  molecules  (then  represented  by  HO)  acquire  a  polarity, 
the  hydrogen  atom,  becoming  charged  with  positive,  and  the  oxygen 
atom  with  negative,  electricity.  The  positive  electrode  then  attracts 
the  negatively  charged  oxygen  atom ;  and  the  negative  electrode,  the 
positively  charged  hydrogen  atom,  causing  the  water  molecules  to 
arrange  themselves  in  the  order  represented  by  the  row  a  in  Figure 
20.  If  now  the  electromotive  force  applied  to  the  electrodes,  and 
the  consequent  charge  of  electricity  upon  the  electrodes,  is  great 
enough,  the  attraction  exerted  on  the  atoms  1  and  1'  nearest  the 
electrodes  causes  the  decomposition  of  their  respective  water  mole- 
cules. Each  of  the  attracted  atoms  then  moves  to  the  electrode 


FIG.  20 

attracting  it,  where  its  charge  is  neutralized  by  the  charge  on  the 
electrode,  and  it  assumes  the  form  of  electrically  neutral  gas.  The 
oxygen  and  hydrogen  atoms  2  and  2'  which  are  thus  left  free  in 
the  solution,  according  to  the  theory,  combine  with  the  hydrogen 
and  oxygen  atoms  3  and  3f  respectively,  of  the  adjacent  water 
molecules,  forming  new  molecules  of  water.  The  action  continues 
with  the  other  water  molecules  between  the  electrodes,  resulting  in 
a  row  of  new  water  molecules,  arranged  as  represented  in  the  row  b 
in  the  above  figure.  Under  the  attractive  forces  of  the  charges  on 
the  two  electrodes,  these  new  molecules  are  then  orientated  like 
those  represented  in  row  a,  and  the  process  proceeds  as  before. 
This  explanation  satisfied  the  scientific  world  for  many  decades. 
The  Conductance  of  Solutions  and  the  Constitution  of  Ions.  —  Soon 
after  Grotthus  advanced  his  theory,  the  question  whether  the  water 
or  the  dissolved  substance  conducted  the  electric  current,  and  the 
question  as  to  what  constitutes  the  positive  and  the  negative  ions, 
were  exhaustively  studied.  The  opinion  was  for  a  long  time  divided. 


46  A   TEXT-BOOK  OF   ELECTRO-CHEMISTRY 

In  general,  it  was  usual  to  avoid  the  former  question  by  simply  stat- 
ing facts  without  involving  any  particular  conception  of  the  process 
of  electrolysis.  For  instance,  it  was  a  common  mode  of  expression 
to  speak  of  "  water  which  by  the  addition  of  sulfuric  acid  has  become 
a  good  conductor,"  i.e.  merely  a  statement  of  experimental  obser- 
vation. The  question  regarding  the  constitution  of  anions  and 
cations  of  various  dissolved  substances  also  was  the  subject  of  con- 
siderable disagreement.  The  opinion  advanced  by  Berzelius  was  the 
first  to  be  universally  accepted.  According  to  this  opinion,  in  the 
case  of  sodium  sulfate,  NaO  •  S03,  NaO  is  the  positive  ion,  or  cation, 
while  S03  is  the  negative  ion,  or  anion.  These  ions  move  to  the 
cathode  and  anode  respectively,  where  they  combine  with-  water 
forming  alkali  and  acid.  Sometime  later  the  view  was  expressed 
that  the  ions  of  this  salt  are  Na  and  S04  instead  of  those  given 
above. 

Both  of  the  questions  considered  in  the  preceding  paragraph 
were  answered  by  an  experiment  performed  by  Daniell.  The  answer 
can,  however,  be  considered  as  decisive  only  in  the  light  of  the  con- 
ceptions then  accepted.  Daniell  electrolyzed  a  solution  of  sodium 
sulfate  and  one  of  sulfuric  acid  simultaneously  in  the  same  circuit, 
and  found  that  the  quantities  of  hydrogen  and  oxygen  liberated 
from  each  solution  were  the  same.  He  found,  further,  that  the 
quantities  of  acid  and  alkali  formed  at  the  electrodes  in  the  salt 
solution  were  equivalent  to  the  above  quantities  of  hydrogen  and 
oxygen.  The  results  of  the  experiments  show  the  conception  of 
Berzelius  regarding  the  ions  of  sodium  sulfate  to  be  untenable. 
According  to  his  conception,  it  would  require  twice  as  much  electric- 
ity to  form  the  above  quantities  of  acid  and  base  and  also  to  set 
free  the  above  quantities  of  hydrogen  and  oxygen  in  the  salt  solu- 
tion as  it  would  to  set  free  the  same  quantities  of  hydrogen  and 
oxygen  in  the  acid  solution.  Since  both  solutions  are  in  the  same 
circuit,  it  is  evident  that  this  is  in  contradiction  to  the  law  of  electro- 
chemical change  (Faraday's  law).  In  agreement  with  this  law, 
Daniell  explained  his  experiment  by  assuming  that  Na  is  the  positive 
and  S04  the  negative  ion,  and  that  these  ions  give  up  their  electric 
charges  at  the  electrodes  and  then  react  with  water,  producing  alkali 
and  hydrogen,  and  acid  and  oxygen  [according  to  the  following 
equations :  — 

2  Na  +  2  HO  =  2  NaO  +  H2  (at  the  cathode) ; 
2  SO4+  2  HO  =  2  HS04-f  O2  (at  the  anode)]. 

It  follows  from  this  theory  that  the  quantities  of  acid  and  alkali 


DEVELOPMENT   OF  ELECTRO-CHEMISTRY  47 

formed  in  the  salt  solution  must  be  equivalent  both  to  the  quantities 
of  hydrogen  and  oxygen  set  free  in  the  same  solution  and  those  set 
free  in  the  acid  solution.  The  requirements  of  the  theory  agree 
then  exactly  with  the  results  obtained  by  experiment.  It  also 
follows  from  this  theory  that  the  salt  alone  must  have  conducted  the 
electricity  through  the  solution;  for  if  the  water  conducted  a  part  of 
the  electricity,  besides  the  hydrogen  set  free  as  a  result  of  the  above 
secondary  and  purely  chemical  reaction,  there  would  be  a  quantity 
of  these  two  gases  set  free  corresponding  to  the  quantity  of  electric- 
ity conducted  by  the  water.  In  this  case  the  quantities  of  acid  and 
alkali  formed  must  always  be  less  than  the  equivalent  of  the  quan- 
tities of  oxygen  and  hydrogen  set  free.  This  is  contradicted  by  the 
experimental  results  already  mentioned. 

Later  experiments  made  by  Hittorf  and  Kohlrausch  confirmed  the 
explanation  of  the  phenomena  of  electrolysis  given  by  Daniell.  Ac- 
cordingly, the  metals  and  radicals  behaving  like  metals,  such  as  H', 
Na ,  IT,  Ag,  Hg,  Hg  ',  Fe-  ',  Fe'  '  ',  NH4',  IsrH3(CH3)-,  etc.,  are 
considered  to  form  positive  ions,  while  all  remaining  atoms  or  groups, 
of  conducting  substances  in  solution,  such  as  OH',  N03',  Cl',  Brf,  I', 
Fe(CN)6' ' ',  Fe(CN)6f '  ",l  etc.,  are  considered  to  form  negative  ions. 
It  is  seen  here  that  there  are  isomeric  ions  of  different  valences 
among  both  the  negative  and  the  positive  ions.  For  instance 
Fe(CN)6' ' '  is  the  negative  ion  of  potassium  ferricyanide,  and 
Fe(CN)6' ' ' ',  its  tetravalent  isomer,  is  the  corresponding  ion  of 
potassium  ferrocyanide.  It  is  by  means  of  such  ions  as  those  given 
above,  formed  almost  entirely  from  the  dissolved  substance,  that 
electricity  is  conducted  through  a  solution.  The  electrical  conductance 
of  a  solution  is,  therefore,  a  property  of  the  dissolved  substance,  the 
solute,  and  not  of  the  solvent. 

Replacement  of  the  Grotthns  Theory  by  the  Clausing  Theory. — 
As  science  gradually  developed,  the  imperfection  of  the  theory  ad- 
vanced by  Grotthus  became  more  and  more  apparent.  According 
to  this  theory  the  splitting  of  the  molecules,  which  is  necessary  for 
the  conduction  of  electricity,  cannot  take  place  until  the  electro- 
motive force  is  sufficiently  great  to  overcome  the  affinity  or  cohesion 
between  the  two  components  of  the  given  compound.  As  a  matter 
of  fact,  however,  it  was  found  that,  under  suitable  conditions  of  ex- 
periment, it  is  possible  to  cause  an  electric  current  to  pass  through 
a  solution  even  when  the  electromotive  force  of  the  current  is  ex- 
tremely small.  For  example,  such  an  electric  current  will  pass 

1  As  recommended  by  Ostwald,  a  dot  is  used  to  denote  a  positive  charge  and 
a  prime  to  denote  a  negative  charge. 


48  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

through  a  solution  of  silver  nitrate  between  silver  electrodes,  causing 
silver  to  dissolve  from  one  electrode  and  to  deposit  upon  the  other. 
The  entire  action  thus  consists  merely  in  the  transfer  of  silver  from 
one  electrode  to  the  other.  It  follows  from  what  has  just  been  said 
that  Ohm's  law  holds  for  all  differences  of  potential,  from  the  small- 
est upward,  in  the  case  of  electrolytic  conduction. 

In  order  to  show  still  more  clearly  the  incompatibility  of  the 
Grotthus  theory  and  experimentally  determined  facts,  let  us  consider 
the  following  illustration :  If  to  each  point  in  a  horizontal  row  of 
points,  a  small  sphere  is  held  with  a  certain  force  X,  then  a  move- 
ment of  the  entire  row  of  spheres  in  a  horizontal  direction,  such 
that  each  sphere  moves  to  the  position  of  the  sphere  in  front  of  it, 
can  only  take  place  by  the  application  of  a  force  sufficiently  great 
to  overcome  the  force  X.  Even  with  the  application  of  such  force, 
a  continuous  "  current "  of  spheres  can  only  be  maintained  when  the 
spheres  moving  away  are  continually  replaced  by  others.  The 
analogy  between  this  "current"  of  spheres  and  the  current  of 
molecules  assumed  by  the  Grotthus  theory  is  at  once  apparent. 

Clausius  was  the  first  to  direct  attention  to  the  disagreement  of 
the  Grotthus  theory  or  conception  of  electrolysis  with  facts.  Basing 
his  conclusions  upon  the  experimental  results  already  mentioned,  he 
declared  "  every  assumption  to  be  inadmissible  which  requires  the 
natural  condition  of  a  solution  of  an  electrolyte  to  be  one  of  equi- 
librium in  which  every  positive  ion  is  firmly  combined  with  its  nega- 
tive ion,  and  which,  at  the  same  time,  requires  the  action  of  a 
definite  force  in  order  to  change  this  condition  of  equilibrium  into 
another  differing  from  it  only  in  that  some  of  the  positive  ions  have 
combined  with  other  negative  ions  than  those  with  which  they  were 
formerly  combined.  Every  such  assumption  is  in  contradiction  to 
Ohm's  law." 

It  is  a  necessary  conclusion  from  the  above  statement  of  Clausius 
that  the  individual  ions  must  exist  uncombined  and  free  to  move  in 
the  solution.  Clausius  himself  was  prevented  from  drawing  this 
conclusion  by  the  prevailing  theories  of  his  time.  He  chose  rather 
to  follow  a  middle  path  by  assuming  that  the  positive  and  negative 
particles  of  a  molecule  of  a  dissolved  electrolyte  were  not  firmly 
combined  with  each  other,  but  were  in  a  state  of  vibration,  and  that 
often  this  vibration  became  vigorous  enough  to  cause  the  positive 
part  of  one  molecule  to  come  into  the  sphere  of  influence  of  the 
negative  part  of  another  molecule,  with  which  it  then,  for  a  time, 
vibrates.  The  positive  and  negative  particles,  thus  left  momentarily 
free,  soon  come  into  the  sphere  of  influence  of  oppositely  charged 


DEVELOPMENT  OF  ELECTRO-CHEMISTRY  49 

parts  of  other  molecules  with  which  they,  also,  for  a  time,  vibrate. 
Thus  there  takes  place  in  a  solution  a  constant  exchange  between 
the  positive  and  negative  parts  of  the  molecules  of  the  dissolved 
electrolytes.  When  now  an  electric  current  flows  through  the  solu- 
tion, an  electrical  force  is  exerted  in  the  direction  of  the  current, 
and  the  vibration  and  exchange  between  the  positive  and  negative 
parts  of  the  molecules  no  longer  take  place  with  entire  irregularity 
as  before,  but  take  place  in  such  a  manner  that  the  vibrations 
become  more  vigorous  and  the  exchanges  more  frequent  in  the 
direction  of  the  action  of  the  electrical  force.  If  a  cross  section  of 
the  solution  be  taken  perpendicular  to  the  direction  of  the  electrical 
force,  then  evidently  more  positive  particles  would  move  through  it 
in  the  direction  of  the  current  of  positive  electricity  or  positive 
direction,  than  in  the  direction  of  the  current  of  negative  electricity 
or  negative  direction,  per  unit  of  time,  and  similarly  more  negative 
particles  would  move  through  it  in  the  direction  of  the  current  of 
negative  electricity  than  in  the  opposite  direction.  There  is,  then, 
a  resultant  motion  of  the  positive  parts  of  the  molecules  in  the 
positive  and  of  the  negative  parts  in  the  negative  direction  through 
the  cross  section.  It  is  by  means  of  this  movement  of  the  two 
oppositely  charged  parts  of  the  molecules  of  the  dissolved  electrolyte 
that  the  electric  current  passes  through  a  solution. 

From  this  discussion  it  is  evident  that,  whereas  Grotthus  assumed 
that  the  electric  current  decomposed  the  dissolved  molecules  of  the 
electrolyte,  Clausius  assumed  that  the  electric  current  merely  guides 
and  hastens  the  charged  parts  of  the  molecules  toward  the  oppo- 
sitely charged  electrodes,  respectively,  during  their  momentary 
periods  of  freedom.  The  latter  theory  was  generally  accepted 
almost  up  to  the  present  time. 

At  about  the  same  time  that  Clausius  advanced  his  theory, 
Hittorf  began  work  upon  the  migration  of  the  ions,  and  a  little 
later  Kohlrausch  commenced  experiments  upon  the  electrical  con- 
ductance of  solutions.  The  work  of  these  investigators  greatly 
increased  the  knowledge  of  the  process  of  the  electrolysis.  Making 
use  of  their  work,  Arrhenius  in  1887  replaced  the  theory  of  vibrating 
ions  of  Clausius  by  the  theory  of  free  ions. 

Relation  between  Chemical  and  Electrical  Energy  I. — When  Volta 
stated  that  electricity  was  produced  at  the  point  of  contact  between 
two  metals  (see  page  33),  the  law  of  the  conservation  of  energy  had 
not  been  advanced,  and  therefore  he  did  not  know  that  the  energy 
of  the  electric  current  could  only  be  produced  at  the  expense  of 
some  other  form  of  energy.  He  considered  perpetual  motion  to  be 


50  A   TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

possible,  and  believed  also  that  an  arrangement  might  be  devised 
which  would  neither  wear  out  nor  require  attention,  and  which, 
moreover,  would  be  capable  of  furnishing  an  unlimited  quantity  of 
electrical  energy.  Since  the  middle  of  the  last  century,  when  the 
law  of  the  conservation  of  energy  was  discovered,  these  views  of 
Volta  of  necessity  have  suffered  a  change.  The  chemical  reactions 
which  take  place  between  metal  and  liquid,  which  earlier  were 
considered  insignificant  phenomena  of  the  electric  current,  are 
now  recognized  as  the  source  of  the  electric  current.  They  furnish 
the  energy  necessary  for  its  production. 

It  is  remarkable  that  the  source  of  the  electromotive  force  of  the 
current  was  assumed  to  be  at  the  point  of  contact  of  the  two  dis- 
similar metals.  Without  the  best  of  reasons,  it  is  clearly  inadmis- 
sible to  consider  that  the  reactions  which  take  place  about  the 
electrodes  are  the  source  of  the  electric  current  and,  at  the  same 
time,  to  consider  that  the  source  of  the  electromotive  force  is  situ- 
ated at  another  point.  It  would  be  quite  as  reasonable  to  assume 
that  when  a  quantity  of  heat  is  generated  at  a  given  point  in  a  cir- 
cuit, the  rise  in  temperature  corresponding  to  it  takes  place  at  a 
different  point.  The  simplest  assumption  is  that  the  source  of  both 
electrical  energy  and  electromotive  force  is  at  the  same  point.  This 
assumption  is  justified  as  long  as  it  is  not  shown  to  be  untenable. 
As  a  matter  of  fact,  with  it,  it  is  possible  to  explain  perfectly  the 
existing  relations.  At  the  present  time,  the  electromotive  force  of  a 
cell  is  considered  to  be  made  up  of  the  sum  of  the  two  potential- 
differences  occurring  at  the  surfaces  of  contact  between  the  two 
electrodes  and  the  liquid. 

After  the  establishment  of  the  law  of  the  conservation  of  energy, 
and  after  it  was  recognized  that  the  processes  which  go  on  in  a 
galvanic  cell  give  rise  to  the  electrical  energy,  the  question  whether 
or  not  the  chemical  energy  involved  in  these  processes,  as  measured 
by  the  heat  which  they  generate,  is  completely  transformed  into 
electrical  energy,  still  remained  to  be  answered. 

The  Daniell  cell  (see  Figure  3)  may  be  represented  by  the  follow- 
ing scheme :  — 

Zn  —  ZnS04  solution  —  CuS04  solution  —  Cu. 

When  the  cell  is  in  operation,  zinc  goes  into  solution  and  copper 
separates  out.  Now  the  heat  generated  by  the  reaction  involved  is 
known  from  thermochemical  measurements.  When  equivalent 
weights  of  the  substances  enter  the  reaction,  it  amounts  to  25,050 


DEVELOPMENT   OF  ELECTRO-CHEMISTRY  51 

calories.  Hence  the  therm ochemical  equation,  involving  two  equiva- 
lents of  the  substances  in  question,  is  as  follows :  — 

CuSO4+  Zn  =  ZnS04-h  Cu  +  2  x  25,050  calories. 

If  now  instead  of  heat  this  reaction  produces  electrical  energy,  the 
quantity  of  the  latter  produced  would  be  the  electrical  equivalent  of 
25,050  calories.  The  quantity  of  electrical  energy  actually  pro- 
duced by  the  cell  can  be  easily  calculated  as  follows :  The  quan- 
tity of  electricity  which  flows  through  the  circuit  when  one 
equivalent  of  copper  is  deposited  is  equal  to  96,540,  or  Q,  coulombs, 
since  it  follows  from  Faraday's  law  that,  whenever  one  equivalent 
of  any  substance  is  dissolved  or  deposited  electrically,  this  quantity 
of  electricity  always  passes  through  the  circuit.  The  electromotive 
force  of  the  cell  in  volts  can  be  measured  and  the  electrical-heat 
equivalent  is  known, 

1  volt-coulomb  =  0.2387  calorie. 

The  electrical  energy  produced  by  the  cell,  expressed  in  calories,  is, 
therefore, 

0.2387  x  96540  x  F  calories. 

The  chemical  energy  of  the  reactions  involved  is  25,050  calories. 
If  the  chemical  energy  is  completely  transformed  into  electrical 
energy,  we  have  the  following  equation :  — 

0.2387  x  96540  x  F  =  25050 ; 
or  F  =  1.087  volts. 

Since  this  value  of  the  electromotive  force  of  the  Daniell  cell  is  very 
nearly  identical  with  the  value  of  the  electromotive  force  found  by 
experiment,  it  may  be  concluded  that  the  chemical  energy  is  com- 
pletely transformed  into  electrical  energy. 

Later  experiments  carried  out  with  other  cells  gave  results  not  in 
agreement  with  this  conclusion.  The  question  was  finally  answered 
by  the  theoretical  and  experimental  investigations  of  Willard  Gibbs, 
P.  Braun,  and  H.  von  Helmholtz.  These  investigators  showed  that 
there  is  usually  a  difference  between  the  chemical  energy  consumed 
in  a  cell  and  the  quantity  of  electrical  energy  given  out  by  it.  This 
difference  is  made  evident  by  an  evolution  or  an  absorption  of  heat 
by  the  cell. 


CHAPTER   III 

THE   THEORY   OF  ELECTROLYTIC   DISSOCIATION 

THE  theory  advanced  by  Arrhenius  in  1887 l  gave  a  great  impulse 
to  electro-chemical  research.  By  means  of  it,  the  relation  between 
well-known  facts  which  formerly  seemed  to  have  nothing  in  com- 
mon became  at  once  evident.  It  has  also  been  an  invaluable  aid  in 
making  further  discoveries.  So  fundamentally  important  has  this 
theory  become,  that  it  is  considered  to  be  the  foundation  of  the 
electro-chemical  science  of  to-day.  Its  development,  and  then  the 
present  status  of  electro-chemistry  in  light  of  the  new  conception, 
will  therefore  be  considered  in  detail. 

In  1887  van't  Hoif  published  an  article  in  the  first  volume  of  the 
Zeitschrift  fur physiJcalische  Chemie  entitled,  "The  Role  of  Osmotic 
pressure  in  the  Analogy  between  Solutions  and  Gases."  In  this  arti- 
cle he  showed,  both  theoretically  and  experimentally,  that  the  gas 
laws  of  constant  pressure-volume  product  (Boyle)  and  of  partial 
pressures  (Gay-Lussac)  apply  also  to  dilute  solutes.  He  also  stated 
the  following  very  important  generalization  of  Avogadro's  principle  : 

The  same  number  of  gaseous  or  of  solute  molecules  are  contained  in 
a  given  volume  of  any  gas  or  of  any  solution,  respectively,  when,  at  the 
same  temperature,  the  gaseous  pressure  and  the  osmotic  pressure  have 
the  same  value. 

The  Laws  and  Theories  relating  to  Osmotic  Pressure.  —  The  mean- 
ing of  the  term  osmotic  pressure  may  be  made  clear  by  a  description  of 
an  experiment.  Consider  an  apparatus,  such  as  is  shown  in  Figure 
21,  consisting  of  a  vessel  A  filled  with  water  and  an  upright  tube 
_B,  open  above  and  closed  by  a  semipermeable  membrane  m  below, 
which  contains  a  quantity  of  an  aqueous  solution  as,  for  example,  of 
sugar.  The  lower  end  of  the  upright  tube  is  then  submerged  in  the 
water  contained  in  A  until  the  water  and  sugar  solution  are  at  the 
same  level  a. 

The  semipermeable  membrane  is  of  such  a  nature  as  to  permit  the 
free  passage  through  it  of  water  but  not  of  sugar  molecules.  Many 
skins  and  precipitates  possess  such  a  semipermeable  nature.  A  pre- 

1  Ztschr.  phys.  Chem.,  1,  631  (1887). 
62 


THEORY  OF  ELECTROLYTIC   DISSOCIATION 


53 


FIG.  21 


cipitated  semipermeable  membrane  may  be  prepared  by  closing  the 

lower  end  of  the  upright  tube  with  a  piece  of  parchment  paper  or  a 

piece  of  unglazed  porcelain,  and  placing  in  the 

tube  a  solution  of  potassium  ferrocyanide  and 

in  the  vessel  A  a  solution  of  copper  sulfate. 

The  two  solutions  then  penetrate  the  pores  of 

the   parchment    or   unglazed   porcelain    from 

opposite   sides,  and,  meeting  within,  form   a 

precipitate  of  copper  ferrocyanide  in  the  pores. 

After  washing  free  from  the  salts  used  in  its 

preparation,  the  membrane  is  ready  for  use. 

With  the  apparatus  thus  completed  and 
ready  for  action,  it  is  observed  that  the  sur- 
face of  the  liquid  in  the  upright  tube  steadily 
rises,  due  to  the  influx  of  water  through  the 
membrane  into  the  sugar  solution.  In  order  to 
prevent  the  water  from  entering  the  upright 
tube  in  this  way,  a  definite  pressure  must  be 
exerted  downward  on  the  surface  of  the  sugar 
solution  in  B.  That  pressure  which  is  just  sufficient  to  hold  the 
level  of  the  liquid  in  the  tube  at  its  original  position  a  is  equal 
to  the  osmotic  pressure  of  the  sugar  solution.  In  the  figure,  the 
hydrostatic  pressure  of  the  liquid  column  ab  is  equal  to  the  osmotic 
pressure.  This  osmotic  pressure  exerted  by  the  molecules  of  solute 
is  analogous  to  the  pressure  exerted  by  gaseous  molecules. 

The  general  equation  expressing  the  laws  of  constant  pressure- 
volume  product  (Boyle)  and  of  partial  pressures  (Gay-Lussac)  and 
the  principle  of  equimolecular  volume  (Avogadro)  for  all  gases  is 

pv  —  nRT, 

where  p  is  the  pressure  exerted  by  a  gas  upon  a  surface  of.  one  square 
centimeter,  v  its  volume,  n  the  number  of  mols  (molecular  weights 
expressed  in  grams),  R  a  constant,  and  T  the  absolute  temperature. 

/V^/l« 

The  expression  ^=  has  a  constant  value  for  one  mol  of  a  perfect  gas, 

independent  of  its  nature  or  concentration.  This  constant  value  is 
represented  by  R,  and  is  called  the  gas  constant.  It  represents  ex- 
perimentally determined  facts,  although  the  theoretical  concept,  the 
mol,  is  involved  indirectly.  Whenever  the  molecular  volume  of  any 
gas  in  cubic  centimeters  is  multiplied  by  its  corresponding  pressure 
in  grams  per  square  centimeters,  and  the  resulting  product  divided 


54  A   TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

by  the  absolute  temperature,  the  value  of  R  is  obtained,  namely, 
84800  =  0.8316  x  108  ergs  =0.0821  liter-atm.  =  1.985  calories. 

An  equation,  identical  in  form  with  the  above  general  gas  equa- 
tion, applies  to  solutes.  A  consideration  of  an  experiment  performed 
by  Pfeffer  will  make  this  evident.  He  found  that  the  osmotic  pres- 
sure P  exerted  upon  an  area  of  one  square  centimeter  by  a  one  per 
cent  sugar  solution  at  6.8°  t  or  279.8°  T  is  equal  to  50.5  centi- 
meters of  mercury  or  50.5  x  13.59  grams.  Since  100  cubic  centi- 
meters of  the  solution  contained  very  nearly  one  gram  of  sugar,  and 
since  one  mol  of  sugar  is  342  grams,  the  volume  of  solution  V  con- 
taining one  mol  of  sugar  is  34,200  cubic  centimeters.  Consequently 
for  this  sugar  solution 


This  value,  within  the  limits  of  experimental  error,  is  identical  with 
the  value  of  the  constant  M,  obtained  from  the  analogous  expression 

^  •     It  is  evident,  from  this  identity  of  the  numerical  value  of  —  - 

and  ^,  that  the  osmotic  pressure  exerted  by  the  dissolved  sugar  mole- 

cules is  equal  to  the  gas  pressure  which  the  same  molecules  would  exert 
if  the  sugar  existed  as  a  gas  in  the  same  volume  and  at  the  same 
temperature. 

Having  considered  the  phenomenon  of  osmotic  pressure  and  the 
laws  which  it  obeys,  it  is  unnecessary  as  far  as  the  phenomenon  it- 
self is  concerned  to  form  special  conceptions  concerning  its  mechan- 
ism. Since,  however,  osmotic  pressure  figures  prominently  in  the 
discussions  in  the  following  pages,  and  since  many  new  conceptions 
are  most  clearly  understood  by  means  of  their  analogy  with  it,  the 
following  hypothetical  discussion  of  the  cause  of  osmotic  pressure  is 
given  :  — 

If  a  sugar  solution  be  placed  in  a  glass  tube  which  is  sealed  at  the 
bottom,  no  evidence  of  osmotic  pressure  is  observable.  At  the  sur- 
face of  the  solution  there  exists  a  pressure,  called  the  internal  pres- 
sure, directed  inward  at  right  angles  to  the  surface,  amounting  to  over 
a  thousand  atmospheres.1  In  the  case  of  a  one  per  cent  sugar  solution 
there  is  a  pressure,  the  osmotic  pressure,  amounting  to  only  about  one 

1  Experimentally  determined  facts,  which  cannot  be  described  here,  have  neces- 
sitated the  recognition  of  such  a  pressure.  Ostwald,  Allgem.  Chem.,  Vol.  II, 
page  538,  second  edition. 


THEORY  OF  ELECTROLYTIC   DISSOCIATION 


55 


atmosphere,  directed  against  this  enormous  internal  pressure.  This 
is  due  to  the  dissolved  sugar  molecules,  which  act  in  the  water  just 
as  they  would  if  they  were  in  the  gaseous  state  and  confined  in  the 
same  volume.  Even  with  very  concentrated  solutions  the  internal 
pressure  is  still  hundreds  of  atmospheres  greater  than  the  osmotic 
pressure.  It  is  because  of  this  that  the  vessel  containing  a  solution 
is  not  broken  by  the  osmotic  pressure  which  is  exerted  in  the  out- 
ward direction  by  the  dissolved  substance.  As  it  is,  only  the  weight 
of  the  solution  itself  exerts  a  pressure  upon  the  walls  of  the  con- 
taining vessel. 

By  the  employment  of  a  semipermeable  membrane,  however,  evi- 
dence of  the  phenomenon  of  osmotic  pressure  may  at  once  be  ob- 
served. As  already  noted,  when  the  upright  tube  in  Figure  21  is 
closed  at  its  lower  end  with  such  a  membrane,  partly  filled  with  a 
sugar  solution,  and  then  set  in  position  as  described,  water  enters 
through  the  membrane  unless  opposed  by  a  pressure  in  the  opposite 
direction  equal  to,  or  greater  than,  the  osmotic  pressure  of  the  solu- 
tion. The  solution  is  bounded  by  its  surface  of  contact  with  air  and 
with  the  walls  of  the  tube  and  by  the  porous  membrane  with  which 
the  solution  forms  no  continuous  surface,  since  it  is  permeable  to 
water.  At  all  the  surfaces  the  internal  pressure  Pin  is  exerted  in- 
ward, and  the  osmotic  pressure  of  the  dissolved  sugar  P  outward, 
while  at  the  membrane,  since  there  is  no  liquid  surface,  only  the  os- 
motic pressure  P  is  exerted.  Because  of  this,  osmotic  pressure  is 
sometimes  defined  to  be  the  pressure  exerted  on  the 
membrane  by  the  dissolved  substance.  Besides  the 
pressure  which  would  be  exerted  if  the  tube  con- 
tained pure  water,  the  solution,  then,  exerts  os- 
motic pressure  which  tends  to  expand  it.  This 
expansion  can  take  place,  however,  only  when,  by 
means  of  a  semipermeable  membrane,  water  can 
enter  the  solution.  It  is  for  this  reason  that  evi- 
dence of  osmotic  pressure  is  observed  only  when  a 
semipermeable  membrane  is  used. 

The  rising  of  the  solution  in  the  tube  due  to 
pressure  exerted  by  the  dissolved  substance  may 
perhaps  be  more  easily  comprehended  by  calling 
to  mind  the  action  of  a  suction  pump. 

[If  water  is  placed  in  the  tube  and  outer  vessel  as  FIG.  22 

shown  in  Figure  22,  it  will  assume  the  same  level 
if  the  downward  pressure  a  and  a'  are  equal.     If,  however,  the 
downward  pressure  a  is  diminished  by  raising  the  piston  p,  water 


56  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

will  flow  through  the  membrane  and  rise  in  the  tube  as  in  the  case 
of  the  suction  pump.  The  same  movement  of  water  would  evi- 
dently take  place  if,  instead  of  decreasing  the  downward  pressure 
a  upon  the  surface  of  the  water  in  the  tube,  an  upward  pressure  a' 
against  the  surface  is  allowed  to  act.  As  already  shown,  such  an  up- 
ward pressure  may  be  produced  by  dissolving  in  the  water  some 
substance,  as,  for  example,  sugar.  Hence  it  is  that  the  osmotic  pres- 
sure, which  is  this  upward  pressure,  causes  the  liquid  to  rise  in  the 
tube.]1 

The  far-reaching  analogy  which  exists  between  the  behavior  of 
gases  and  of  dilute  solutes  was  first  pointed  out  by  van't  Hoff.  He 
was  also  able  to  deduce,  from  the  laws  of  osmotic  pressure,  analogous 
laws  applying  to  phenomena,  which,  apparently,  were  not  related  to 
osmotic  pressure,  such  as,  for  instance,  the  lowering  of  the  vapor 
pressure  or  of  the  freezing  point  of  a  solvent  by  dissolving  a  sub- 
stance in  it.  The  laws  followed  by  these  phenomena  had  already 
been  empirically  established,  principally  by  Raoult.  They  may  be 
expressed  as  follows  :  — 

The  lowering  of  the  vapor  pressure  or  of  the  freezing  point  of  a  solvent 
caused  by  a  dissolved  substance  is  directly  proportional  to  its  concentra- 
tion. The  lowering,  in  each  case,  for  a  given  solvent  is  the  same  for 
equimolar  solutions  of  all  substances.  Equimolar  solutions  contain, 
in  the  same  quantity  of  solvent,  such  quantities  of  dissolved  sub- 
stances, respectively,  as  are  proportional  to  their  molecular  weights. 
These  laws  made  possible  a  considerable  increase  in  the  knowledge 
of  the  constitution  of  matter,  especially  in  regard  to  the  molecular 
weights  of  solutes,  or  substances  in  solution.  Previously,  molecular 
weights  could  be  determined  only  in  the  case  of  those  substances 
which  could  be  volatilized  without  undergoing  chemical  change. 

The  laws  of  constant  pressure-volume  product  (Boyle-Mariotte) 
and  of  partial  pressures  (Gay-Lussac)  are  laws  of  a  limiting  condi- 
tion, holding  strictly  only  for  gases  at  extreme  dilution.  Therefore, 
from  the  analogy  which  exists  between  gaseous  and  osmotic  pres- 
sures, it  would  be  expected  that  deviations  from  the  simple  laws  of 
solutions  would  be  found  in  the  case  of  concentrated  solutions. 
Such  has  indeed  been  found  to  be  the  case  when,  as  has  been  the  cus- 
tom, the  volume  involved  was  taken  equal  to  that  of  the  solution. 
Recently,  however,  very  surprising  results  have  been  obtained  by 
Morse  and  Frazer2  in  their  experimental  work  on  osmotic  pressure. 

1  For  a  more  exact  definition  of  osmotic  pressure,  see  Planck,  Ztschr.  phys. 
Chem.,42,  584  (1903). 

2  Ztschr.  Elektrochem.,  11,  621  (1905). 


THEORY  OF  ELECTROLYTIC   DISSOCIATION  57 

They  found  that,  even  for  concentrated  solutions  (over  30  %),  the 
following  statement  holds  :  — 

The  osmotic  pressure  exerted  by  cane  sugar  in  water  solution  is  equal 
to  that  which  it  would  exert  at  the  same  temperature  if  it  existed  as  a 
perfect  gas  expanded  in  the  volume  occupied  by  the  pure  solvent. 

Calculating  in  a  similar  manner,  it  has  also  been  found  that  the 
freezing-point  lowering  is  normal  even  for  concentrated  solutions. 
We  may  well  be  impatient  to  see  whether  or  not  this  relation,  which 
is  without  analogy  in  the  gaseous  state,  obtains  generally. 

Abnormality  of  Acids,  Bases,  and  Salts.  Electrolytic  Dissocia- 
tion. —  One  great  difficulty  presented  itself,  and  cast  a  dark  shadow 
upon  the  otherwise  bright  theory  of  solutions.  Almost  all  acids,  bases, 
and  salts  which  are  soluble  in  water  produce  in  water  solutions  a 
much  greater  osmotic  pressure,  vapor-pressure  lowering,  and  freezing- 
point  lowering  than  that  calculated  on  the  assumption  that  the  mo- 
lecular weights  derived  from  a  study  of  their  vapor  densities  and 
chemical  properties  are  correct.  Corresponding  to  the  abnormality 
of  these  properties,  the  values  of  the  molecular  weights  of  these  sub- 
stances calculated  from  these  properties  are,  of  course,  abnormally 
low. 

Not  very  long  before,  the  molecular  theory  of  gases  had  been  in  a 
similar  position,  because  of  the  deviations  of  the  vapor  densities  of 
a  number  of  substances  from  the  requirements  of  the  theory.  It  was 
only  with  considerable  hesitancy  that  the  explanation  of  these  ab- 
normal values  on  the  assumption  of  a  dissociation  of  the  molecules 
of  the  gases  was  then  accepted,  although  at  the  present  time  the  cor- 
rectness of  this  assumption  is  never  doubted.  Certainly,  it  was  nat- 
ural in  the  light  of  the  close  analogy  known  to  exist  between  the 
gaseous  and  the  dissolved  state,  to  assume  that  in  solution  a  similar 
dissociation  takes  place.  From  thermodynamical  considerations, 
the  physicist  Planck  concluded  that  such  a  dissociation  does  take 
place.1  This  conclusion  was  not,  however,  shared  by  chemists.  In- 
deed, such  a  supposition  seemed  absurd,  for  it  required  that  sub- 
stances like  potassium  chloride,  in  which  the  atoms  were  considered 
to  be  held  together  by  the  strongest  chemical  affinity,  should  sponta- 
neously decompose  and  exist  in  water  solution  as  potassium  and 
chlorine,  in  spite  of  the  fact  that  metallic  potassium  reacts  very  en- 
ergetically with  water.  Moreover,  the  supposition  seemed  to  be  con- 
tradicted by  the  law  of  the  conservation  of  energy ;  for  it  apparently 
implied  that  substances  which  combine  energetically  with  the  gen- 
eration of  much  heat  may  separate  again  spontaneously. 
1  Ztschr.  phys.  Chem.,  1,  577  (1887). 


58  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

Before  such  a  radical  change  could  be  made  in  the  conceptions  of 
the  constitution,  in  water  solution,  of  these  important  classes  of 
compounds,  it  was  necessary  to  remove  the  apparent  contradictions 
of  the  new  conception  to  laws  of  well-proven  validity,  and  also  to 
present  strong  evidence  of  its  correctness.  This  was  done  by 
Arrhenius. 

In  an  early  investigation  of  the  electrical  conductance  of  electro- 
lytes, Arrhenius  had  already  recognized  two  kinds  of  solute  molecules, 
namely,  active  molecules  which  caused  the  electrical  conductance, 
and  the  inactive  molecules.  He  also  expressed  the  opinion  that  at 
extreme  dilution  all  the  inactive  would  be  transformed  into  active 
molecules.  He  recognized  an  "  activity  coefficient "  of  a  solution 
which  is  denned  by  the  equation, 

Number  of  active  molecules  =aotivit    coefficient. 
Total  number  of  molecules 

At  infinite  dilution  the  value  of  this  coefficient  would,  then,  be  unity. 
For  all  other  dilutions,  it  would  be  less  than  unity  and  would  express 
the  ratio  of  the  equivalent  conductance  at  a  given  dilution  to  the 
limiting  value  of  the  equivalent  conductance,  or  the  equivalent 
conductance  at  infinite  dilution.  He  had  not  then  shown  in  what 
respect  the  active  molecules  differ  from  the  inactive.  As  soon  as 
the  above-mentioned  works  of  van't  Hoff  appeared,  Arrhenius  was 
able,  by  comparing  the  freezing-point  lowering  produced  by  electro- 
lytes with  the  electrical  conductance  of  their  solutions,  to  adduce 
remarkable  and  convincing  evidence  of  the  correctness  of  the  theory 
of  electrolytic  dissociation. 

Calculation  of  the  Degree  of  Dissociation.  —  As  already  stated, 
there  is  a  class  of  compounds,  such  as  sodium  chloride,  for  example, 
which  give  an  abnormally  large  lowering  of  the  freezing  point. 
Thus  while  one  mol  of  sugar  dissolved  in  ten  liters  of  water  lowers 
the  freezing  point  by  about  0.186°,  one  mol  of  sodium  chloride  (con- 
sidered as  NaCl),  dissolved  in  the  same  volume,  lowers  it  by  nearly 
twice  that  value.  It  is  evident  that,  if  van't  Hoff's  principle  be 
accepted  as  applying  to  this  case,  and  the  sodium  chloride  be  con- 
sidered as  dissociated  in  solution  into  a  sodium  and  a  chlorine  part, 
the  extent  of  this  dissociation  may  be  calculated  from  a  knowledge 
of  the  deviation  of  the  freezing-point  lowering  of  the  salt  from  the 
freezing-point  lowering  of  an  undissociated  substance. 

j   ,  Abnormal  freezing-point  lowering  __  . 

Normal  freezing-point  lowering 


THEORY   OF  ELECTROLYTIC   DISSOCIATION  59 

where  the  abnormal  value  is  the  value  actually  determined,  and  the 
normal  value  that  which  would  be  obtained  if  the  salt  was  entirely 
undissociated. 

Then  i  =  1  —  x  +  nx, 

where  x  represents  the  degree  of  dissociation  and  n  the  number  of 
parts  into  which  one  molecule  dissociates.  For  the  salt  NaCl,  n  is 
equal  to  2,  and  for  MgCl,  3,  and  so  on. 

The  degree  of  dissociation  x  is  then  given  by  the  equation, 


Arrhenius  calculated  the  degree  of  dissociation,  or,  as  he  called  it, 
the  affinity  constant,  for  a  great  many  substances  from  the  known 
values  of  their  freezing-point  lowering,  and  found  that  the  results  so 
obtained  agreed  with  the  dissociation  values  which  he  obtained  from 
measurements  of  the  electrical  -conductance.  It  follows  from  this, 
that  only  those  substances  in  water  solution  conduct  the  electric  current 
which  are  to  some  degree  dissociated,  and  that  the  greater  the  degree  of 
dissociation  the  more  readily  does  the  substance  conduct  the  electric 
current  It  is  a  logical  conclusion  from  these  statements  that  the 
conductance  of  a  solution  is  due  entirely  to  dissociated  parts  of  the 
molecules.  Arrhenius  ascribed  electrical  charges  to  these  dissociated 
parts  and  called  them  ions. 

Even  at  that  time  Arrhenius  called  attention  to  the  fact  that  many 
other  physical  and  chemical  phenomena  were  very  clearly  explained 
upon  the  assumption  of  the  existence  of  free  ions  in  solution. 

Dissimilarity  between  Gaseous  and  Electrolytic  Dissociation.  The 
Ions.  —  It  is  evident  that  there  is  an  important  difference  between 
dissociation  in  the  dissolved  and  that  in  the  vapor  state,  as,  for 
instance,  in  the  case  of  ammonium  chloride  vapor.  In  the  former 
case  only  are  the  parts  of  molecules  resulting  from  dissociation 
charged  with  electricity.  The  question  at  once  arises  as  to  the 
source  of  these  charges  of  electricity  which  appear  suddenly  when 
an  electrolyte  is  dissolved  in  water.  They  seem  to  be  produced 
from  nothing.  It  is  not  difficult  to  give  a  satisfactory  answer  to  this 
question,  as  will  be  evident  from  the  following  theoretical  discussion. 
Consider,  for  example,  equivalent  quantities  of  the  elementary  sub- 
stances, sodium  and  iodine.  They  possess  definite  quantities  of 
chemical  and  internal  energy.  If  now  they  be  allowed  to  react 
with  each  other  to  form  sodium  iodide,  they  lose  a  portion  of  their 
chemical  or  internal  energy  in  the  form  of  heat.  The  rest  of  the 


60  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

energy  originally  possessed  by  the  sodium  and  iodine  remain  asso 
ciated  with  the  salt,  sodium  iodide,  until  some  further  change  is 
allowed  to  take  place.  If  the  salt  be  dissolved  in  water,  it  dissoci- 
ates to  a  large  extent,  and  the  chemical  or  internal  energy  is  again 
decreased,  this  time  with  the  appearance  of  the  equivalent  quantity 
of  electrical  energy  in  the  form  of  equivalent  positive  and  negative 
charges  on  the  sodium  and  iodine  ions,  respectively.  It  is  evident 
from  this  discussion  that  the  sodium  and  iodine  ions  differ  from  the 
elementary  substances,  sodium  and  iodine,  in  that  they  possess  elec- 
trical energy,  and  also  in  that  their  energy  content  is  less.  They 
may  be  transformed  into  the  corresponding  elementary  substances 
again  by  supplying  electrical  energy  to  them  by  means  of  an  electric 
current  under  suitable  conditions.  When  the  ions  have  taken  up 
the  requisite  quantity  of  energy,  a  transformation  of  electrical  into 
chemical  energy  takes  place,  and  the  sodium  and  iodine  separate  at 
the  electrodes  as  elementary  substances. 

We  may  now  inquire  into  the  cause  of  this  transformation  of 
chemical  into  electrical  energy  when  sodium  iodide  is  dissolved  in 
water,  and  also  question  the  possibility  of  positively  and  negatively 
charged  particles  existing  together  in  a  solution  without  neutralizing 
each  other.  This  inquiry  and  this  question  is  briefly  answered  by 
an  assumption  of  the  theory  of  electrolytic  dissociation.  TJiis 
assumption  states  that  the  solvent  possesses  the  power  of  causing  this 
transformation  of  energy  and  of  preventing  the  mutual  neutralization  of 
the  ions.  It  may  be  questioned  further  whether  the  assumption  of 
electrically  charged  particles  is  of  value  to  science.  Experience  up 
to  the  present  time  answers  this  question  emphatically  in  the  affir- 
mative. 

lonization  according  to  the  Material  Conception  of  Electricity.  — 
According  to  the  material  conception  of  electricity  indicated  in  the 
note  at  the  bottom  of  page  26,  an  ion  may  be  considered  to  be  a  com- 
pound of  positive  or  negative  electrons  with  the  element  in  question. 
These  two  new  elements,  or  electrons,  are  represented  by  the  sym- 
bols, 0  and  0.  The  formation  of  an  ion  is,  then,  entirely  analogous 
to  the  formation  of  a  compound  from  two  ordinary  elements.  For 
instance,  in  the  formation  of  ions  from  sodium  iodide,  the  sodium 
atoms  combine  with  positive  and  the  iodide  atoms  with  negative 
electrons  according  to  the  reaction, 

Nal  +  0  +  0  =  Na0  + 10  =  Na'  + 1'. 
This  conception  is  very  comprehensive,  for,  according  to  it,  the  law 


THEORY  OF  ELECTROLYTIC  DISSOCIATION  61 

of  electro-chemical  change  (Faraday's  law,  see  page  42)  appears  as 
a  consequence  of  the  laws  of  definite  and  multiple  proportion. 

Although  the  theory  of  electrolytic  dissociation  was  not  spared 
great  opposition  in  its  early  years,  it  has  successfully  advanced  until 
at  the  present  time  by  far  the  greater  number  of  investigators  accept 
it  and  recognize  its  value.  As  a  matter  of  fact,  it  possesses  the  ad- 
vantages to  be  expected  of  a  good  theory.  It  correlates  a  large  number 
of  apparently  unrelated  facts  and  serves  as  a  good  guide  for  new  in- 
vestigations. At  present  there  is  no  other  theory  dealing  with  the 
same  subject  that  even  approaches  this  one  in  usefulness,  and  for 
this  reason  it  will  be  applied  throughout  the  book.  However,  it 
should  be  borne  in  mind  that  it  is  a  theory  and  not  a  dogma  that  is  in- 
volved, the  conclusions  from  which  must  be  impartially  tested  by  experi- 
mentally determined  facts. 


CHAPTER   IV 

THE  MIGRATION   OF  IONS 

ACCORDING  to  the  dissociation  theory,  electrolytes  exist  in  aqueous 
solution  partly  in  the  form  of  ions,  each  of  which  possesses  a  definite 
electrical  charge.  For  example,  in  a  solution  of  hydrochloric  acid 
there  are  hydrogen  ions,  H',  charged  with  a  definite  quantity  of  posi- 
tive, and  chlorine  ions,  Cl',  charged  with  an  equivalent  quantity  of 
negative,  electricity.  Calling  to  mind  the  law  of  electro-chemical 
change,  or  Faraday's  law,  it  may  be  stated,  first,  that  the  conduction 
of  electricity  through  a  solution  takes  place  only  by  means  of  a 
movement  of  those  ponderable  particles  which  are  charged  with 
electricity  (in  the  above  case,  the  hydrogen  and  chlorine  ions)  ;  and 
second,  that  chemically  equivalent  quantities  of  these  particles  are 
charged  with  equal  quantities  of  electricity. 

A  galvanic,  or,  what  is  the  same  thing,  an  electric,  current  may  be 
produced  in  an  electrolyte  by  dipping  into  it  two  electrodes  which 
are  connected  with  the  positive  and  negative  poles,  respectively,  of  a 
source  of  electricity.  In  consequence  of  the  potential-difference  thus 
produced  between  the  two  electrodes,  the  positive  and  negative  ions 
move  in  opposite  directions  toward  their  respective  electrodes,  and 
an  electric  current  is  said  to  flow  through  the  solution.  In  all  cases 
the  passage  of  the  electric  current  is  accompanied  by  a  decomposition 
of  the  electrolyte,  even  though,  in  case  of  a  very  feeble  current,  it 
may  not  be  evident.  With  hydrochloric  acid,  electrically  neutral 
hydrogen  and  chlorine  gases  separate  at  the  cathode  and  anode, 
respectively.  An  electric  current  can  also  be  produced  in  a  solution 
by  induction  without  the  use  of  electrodes.  In  this  case  no  transfor- 
mation from  the  ionic  to  the  electrically  neutral  state  takes  place. 

When  an  electric  current  is  conducted  through  a  solution,  a  certain 
number  of  positive  ions  pass  through  a  cross  section  of  the  solution 
between  the  electrodes  in  one  direction,  and  simultaneously  a  certain 
number  of  negative  ions  pass  through  it  in  the  opposite  direction. 
It  was  formerly  believed  that  when  the  two  ions  possessed  the  same 
valency,  the  same  number  of  positive  and  negative  ions  pass  through 
a  cross  section  in  a  given  time.  This  belief  owed  its  existence 


THE  MIGRATION  OF  IONS  63 

undoubtedly  to  the  fact  that  the  quantities  of  the  constituents  of 
the  electrolyte  which  separate  at  the  two  electrodes  are  equivalent 
to  each  other.  It  is  now  known,  however,  that  seldom  or  never  do 
equal  numbers  of  the  two  kinds  of  ions  pass  through  a  cross  section 
of  the  solution  in  the  same  time.  The  phenomena  of  electrical  con- 
duction and  decomposition  are  not  as  closely  related  as  was  formerly 
believed.  Their  relation  was  discovered  by  Hittorf  *  by  a  careful 
study  of  the  changes  in  the  concentration  of  an  electrolyte  which 
take  place  about  the  electrodes,  during  the  passage  of  an  electric 
current. 

It  will  now  be  explained  how  a  knowledge  of  the  relative  numbers 
of  the  two  kinds  of  ions  passing  a  cross  section  in  a  given  time,  or, 
what  is  the  same  thing,  a  knowledge  of  the  relative  velocities  of 
migration  of  the  two  kinds  of  ions,  can  be  obtained  from  a  study  of 
the  concentration  changes  just  mentioned. 

As  already  stated,  whenever  a  current  of  electricity  passes  through 
a  solution  of  an  electrolyte,  such  as  of  hydrochloric  acid,  a  move- 
ment of  ions,  and  a  decomposition  at  the  electrodes,  takes  place.  It 
follows  also  that,  in  a  solution  of  such  an  electrolyte,  there  are  always 
the  same  number  of  negative  and  positive  ions ;  for  if  a  negative  ion 
separates  on  the  positive  electrode  as  an  electrically  neutral  sub- 
stance without  the  simultaneous  separation  of  a  positive  ion  at  the 
negative  electrode,  the  solution  afterwards  contains  more  positive 
than  negative  ions  and  hence  contains  an  excess  of  positive  electric- 
ity. This  excess  of  positive  electricity  is  large,  since  the  electrical 
charge  upon  an  ion  is  very  great.  If  still  another  negative  ion  is  to 
be  separated  alone  at  the  electrode,  a  greater  quantity  of  work  would 
be  required  than  before,  because  the  positively  charged  solution 
would  now  have  a  greater  attraction  for  the  negative  ion  and  there- 
fore would  resist  its  separation  more  strongly  than  before.  On  the 
other  hand,  the  separation  of  a  positive  ion  at  the  other  electrode 
would  require  very  little  work  because  of  the  repellent  force  of  the 
positive  electricity  of  the  solution.  Since  this  electrostatic  force, 
compared  to  the  other  forces  involved,  is  very  great,  the  decomposi- 
tion of  the  electrolyte  must  take  place  in  such  a  manner  that  the 
positive  and  negative  ions  always  leave  the  solution  at  such  rates 
that  the  solution  itself  remains  electrically  neutral. 

The  necessity  of  the  separation  of  equivalent  quantities  of  the 
two  kinds  of  ions  at  the  electrodes  has  now  been  demonstrated.  It 
is  known  from  electrical  science  that  the  current,  or  the  quantity  of 

1  Pogg.  Ann.,  89,  98,  103,  106  (1853  and  1859).  A  reprint  of  this  work  may 
be  found  in  Ostwald's  Klassiker  d.  exakt.  Wiss.,  Nos.  21  and  23. 


64  A   TEXT-BOOK  OF   ELECTRO-CHEMISTRY 

electricity  passing  through  a  cross  section  of  the  solution  of  the  elec- 
trolyte per  unit  of  time,  is  the  same  at  all  points  of  the  circuit.  It 
is  evident  also  that  the  total  quantity  of  electricity  in  motion  is 
equal  to  the  sum  of  the  positive  and  negative  electricities  flowing  in 
the  circuit,  but  it  does  not  follow  that  the  ratio  of  the  positive 
to  the  negative  electricity  must  remain  the  same  throughout  the 
circuit.  Indeed,  without  contradicting  the  teachings  of  electrical 
science,  it  may  even  be  assumed  that  in  a  given  circuit  the  total 
quantity  of  electricity  1,  is  made  up  of  \  positive  and  \  negative  at 
one  point,  of  \  positive  and  }  negative  electricity  at  another,  and  so 
on.  Since  the  motion  of  one  kind  of  electricity  in  one  direction  pro- 
duces the  same  effects  as  the  motion  of  the  other  kind  in  the  oppo- 
site direction,  it  is  justifiable  to  consider  the  total  quantity  of  elec- 
tricity in  motion  as  flowing  in  one  direction,  although,  in  reality,  any 
portion  of  the  total  quantity  may  be  flowing  in  one  direction  while 
the  rest  of  it  is  flowing  in  the  other.  It  is  evident  from  these  state- 
ments that  there  is  no  necessity  for  assuming  equal  velocities  for 
the  different  ions.  This  would  only  be  the  case  when  there  is  a 
motion  of  equal  quantities  of  positive  and  negative  electricities  at 
the  same  rate  in  opposite  directions. 

As  a  matter  of  fact,  seldom  or  never,  when  an  electric  current  is 
flowing  through  a  solution  of  an  electrolyte,  do  equivalent  quantities 
of  positive  and  negative  ions  pass  through  a  cross  section  of  the 
solution  in  a  given  time.  This  is  due  to  the  fact  that  the  mobili- 
ties of  the  two  kinds  of  ions  are  never  the  same.  Thus  the 
mobility  of  the  chlorine  ion  is  far  less  than  that  of  the  hydrogen  ion. 
Corresponding  to  this  difference  in  mobility,  when  the  two  ions  are 
subjected  to  the  action  of  forces  of  the  same  magnitude,  as  is  the 
case  in  the  electrolysis  of  a  solution  of  hydrochloric  acid,  the  hydro- 
gen ion  moves  about  five  times  as  fast  as  the  chlorine  ion.  It  must, 
however,  be  remembered  that  the  number  of  positive  ions  is  always 
equal  to  the  number  of  negative  ions  not  only  in  the  whole  solution, 
but  also,  in  general,  in  every  part  of  the  solution. 

It  will  be  seen  later  on  that  it  is  possible  to  correlate  a  large  num- 
ber of  facts  concerning  electrolysis  by  the  assumption  that  the  differ- 
ent ions  migrate  with  different  velocities. 

The  motion  or  migration  of  the  two  kinds  of  ions  may  be  made 
more  comprehensible  by  a  comparison  with  the  movements  of  two 
columns  of  cavalrymen  which  are  passing  each  other.  Suppose  one 
column  proceeding  at  a  walk,  the  other  at  a  gallop,  and  imagine  a 
ditch  in  the  way  which  both  columns  are  crossing  at  the  same  time. 
If  the  second  column  moves  five  times  as  rapidly  as  the  first,  then 


THE   MIGRATION  OF  IONS  65 

five  horsemen  of  the  former  column  cross  the  ditch  in  one  direction 
in  a  certain  time,  while  one  of  the  latter  column  crosses  it  in  the  other 
in  the  same  time.  In  all  six  horsemen  pass  the  ditch.  If  each 
horseman  carries  100  grams  of  powder,  then,  during  this  time,  600 
grams  of  powder  is  transported  across  the  ditch,  500  grams,  or  £  of 
it,  in  one  direction  and  100  grams,  or  i  of  it,  in  the  other.  In  this 
illustration  the  two  columns  of  cavalrymen  represent  the  two  kinds 
of  particles  or  ions,  and  the  100-gram  portions  of  powder,  the  elec- 
trical charge  which  each  particle  or  ion  carries.  The  case  may  now 
be  considered  in  which  the  cavalrymen  and  portions  of  powder  are 
replaced  by  ions  and  electric  charges. 

If  a  current  of  electricity  be  passed  through  a  solution  of  hy- 
drochloric acid  between  platinum  electrodes,  as  already  stated,  the 
hydrogen  ions  migrate  in  one  direction  with  five  times  the  velocity 
with  which  the  chlorine  ions  migrate  in  the  opposite  direction. 
Hence  when  the  quantity  of  electricity  6  passes  through  the  solution, 
the  quantity  5,  or  £  of  it,  is  carried  by  the  hydrogen  ions,  and  the 
quantity  1,  or  £  of  it,  by  the  chlorine  ions.  [This  will  be  more 
evident  from  a  consideration  of  the  following  diagrams,  in  which 


FIG.  23 

the  hydrogen  ions  are  represented  by  the  symbol  +,  and  the  chlo- 
rine ions  by  the  symbol  — ,  and  the  directions  in  which  the  ions 
move  when  an  electric  current  is  passing  are  indicated  by  arrows. 
In  Figure  23  a  line  of  twenty-one  pairs  of  hydrogen  and  chlorine 
ions  are  represented  between  the  two  electrodes,  five  of  which  are 
situated  between  the  two  porous  diaphragms  D  and  D,  which  are 
permeable  to  the  ions  and  merely  serve  to  prevent  the  stirring  of 
the  solution  by  convection  currents.  This  represents  the  condition 
of  the  solution  before  an  electric  current  has  passed.  If  now  a 
quantity  of  electricity  is  passed  through  the  solution  sufficient  to 
separate  at  the  two  electrodes  six  ions  of  chlorine  and  six  of  hy- 
drogen, and  if  the  hydrogen  ions  move  five  times  as  fast  as  the 
chlorine  ions,  the  condition  of  the  solution  at  the  end  of  the  elec- 
trolysis is  represented  by  Figure  24. 

Here  it  is  seen  that  five  hydrogen  ions  have  passed  from  the  anode 


66 


A   TEXT-BOOK  OF   ELECTRO-CHEMISTRY 


section  into  the  middle  section,  and  the  same  number  from  the 
middle  section  into  the  cathode  section,  and  that  in  the  same  way 
one  chlorine  ion  has  passed  in  the  opposite  direction  from  the 
cathode  section  and  one  has  appeared  in  the  anode  section.  Since 
each  ion  carries  the  same  quantity  of  electricity,  it  is  evident  that 
|  of  the  total  quantity  is  carried  through  the  middle  section  by 
the  hydrogen  ions,  and  £  by  the  chlorine  ions.  The  number  of 
ions  in  the  middle  section  has  remained  constant  and  need  not  be 
further  considered.  From  the  anode  section  six  chlorine  ions 
(shown  in  the  vertical  column)  have  given  up  their  charges  to  the 
anode  and  assumed  the  state  of  gaseous  chlorine,  while  from  the 
cathode  section  six  hydrogen  ions  (vertical  column)  have  similarly 
given  up  their  charges  and  assumed  the  state  of  gaseous  hydrogen. 
The  particles  of  the  inert  gases  are  represented  by  dots  on  the  elec- 
trode surface.  The  anode  section  has  then  received  by  migration  to  it 
one  chlorine  ion,  and  has  lost  by  migration  from  it  five  hydrogen  ions 
and  by  separation  at  the  anode  six  chlorine  ions.  The  concentration 
in  the  anode  section  has  then  decreased  from  eight  pairs  of  ions 
to  three  pairs.  From  a  similar  consideration  it  may  be  shown  that 


D|>              D| 

-^V 

I        + 

. 

f 

-    "  '.Middle 
~        Anode  Section                 Section               Cathode  Section       ' 

FIG.  24 

the  concentration  in  the  cathode  section  has  decreased  from  eight 
pairs  of  ions  to  seven  pairs.  Therefore  the  loss  in  concentration  in 
the  anode  section  is  to  the  loss  in  the  cathode  section  as  five  is  to 
one.  But  this  is  also  the  ratio  of  the  velocity  of  the  hydrogen  to 
that  of  the  chlorine  ion.  Hence  the  following  relation  exists  be- 
tween the  losses  in  concentration  in  the  two  sections  and  the  corre- 
sponding velocities  of  the  two  ions  : 

Loss  in  the  anode  section         Velocity  of  the  cation  "1 
Loss  in  the  cathode  section         Velocity  of  the  anion  J 

Only  at  the  surfaces  where  the  current  passes  to  or  from  the  elec- 
trode does  the  migration  of  a  single  kind  of  ion  take  place.  At  these 
surfaces  the  conduction  of  the  current  consists  in  the  passage  of  a 
given  quantity  of  negative  electricity  directly  to  the  anode,  while 
simultaneously  an  equivalent  quantity  of  positive  electricity  passes 


THE  MIGRATION   OF  IONS 


6T 


directly  to  the  cathode.  This  explains  the  fact  that  the  quantity  of 
the  substances  which  separate  at  the  electrodes,  while  dependent 
upon  the  quantity  of  electricity  which  passes,  is  independent  of  the 
velocity  of  migration  of  the  ions  and  all  other  circumstances,  and 
explains  also  the  fact  that  changes  occur  in  the  concentration  of  the 
solutions  about  the  electrodes  during  electrolysis. 

The  mechanism  of  electrolysis  being  thus  illustrated,  an  actual 
problem  will  now  be  explained.  Consider  the,  vessel  shown  in  Fig- 
ure 25,  which  is  divided  into  three  equal  parts  by  means  of  porous 


D 

Ij 

—> 

Anode 

Middle 

Cathode 

Section. 

Section 

Section 

FIG.  25 

plates  permeable  to  ions,  to  be  filled  with  a  solution  containing  30 
equivalents  of  hydrochloric  acid.  In  each  compartment  of  the  ves- 
sel there  are,  then,  10  equivalents  of  the  acid.  If  now  96,540  cou- 
lombs of  electricity  are  passed  through  the  solution,  1  equivalent 
of  hydrogen  will  separate  at  the  cathode,  and  1  of  chlorine  at  the 
anode.  This  quantity  of  these  gases  may  be  considered  to  be 
removed  from  the  solution.  Since  the  same  quantity  of  electricity 
passes  through  every  cross  section  of  a  circuit,  96,540  coulombs  pass 
through  the  cross  sections  of  the  solution,  I  and  II. 

If  it  is  assumed  that  both  ions  migrate  with  the  same  velocity, 
then  ^  of  an  equivalent  of  hydrogen  ions,  carrying  48,270  coulombs, 
passes  from  the  anode,  through  the  middle,  and  to  the  cathode 
section,  and  simultaneously  \  of  an  equivalent  of  chlorine  ions,  also 
carrying  48,270  coulombs,  passes  the  section  in  the  reverse  order. 
The  gain  or  loss  in  concentration  in  the  three  sections,  due  to  the 
electrolysis,  may  now  be  found.  The  cathode  section  has  lost  1 
equivalent  of  hydrogen  ions  by  separation  as  a  gas  at  the  cathode, 
and  ^  of  an  equivalent  of  chlorine  ions  by  migration  to  the  anode, 
and  has  gained  ^  of  an  equivalent  of  hydrogen  ions  by  migration 
from  the  anode.  It  has  therefore  suffered  a  final  loss  of  £  an  equiv- 
alent of  hydrochloric  acid,  and  therefore  contains,  after  the  elec- 
trolysis, 9J  equivalents  of  the  acid.  Similarly  it  may  be  shown  that 


68 


A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 


the  concentration  of  the  solution  in  the  anode  section  has  decreased 
to  9^-  equivalents.  The  middle  section  has  not  suffered  a  change  in 
concentration,  since  equal  quantities  of  the  two  ions  have  migrated 
to  and  from  it.  [The  following  summary  may  serve  to  make  the 
above  concentration  changes  more  comprehensible :  — 

Original  concentration  in  each  section  =  10  equiv.  HC1, 
Quantity  of  electricity  passed  =    96,540  coulombs. 


ANODE  SECTION 

MIDDLE  SECTION 

CATHODE  SECTION 

Eq.  H' 

Eq.  Cl' 

Eq.  H1 

Eq.  Cl' 

Eq.H' 

Eq.  Clw 

Loss  by  separation 
Loss  by  migration 
Gain  by  migration 

Total  loss 

i 

1 

1 

* 
1 

I 
\ 

1 

i 

i 

1 

i 

0 

0 

1 

\ 

Final  cone.  H'  Cl'                            9£ 

10 

n       } 

It  follows,  then,  that  when  the  velocity  of  migration  of  the  two  ions 
is  the  same,  the  solution  in  both  the  anode  and  the  cathode  section 
will  suffer  the  same  change  in  concentration. 

The  hydrogen  ions,  however,  really  migrate  about  five  times  as 
fast  as  the  chlorine  ions.  The  above  consideration  will  now  be 
altered  as  required  for  this  case.  Accordingly,  f  of  an  equivalent 
of  hydrogen  passes  from  the  anode,  through  the  middle,  to 
the  cathode  section,  carrying  with  it  £  of  96,540  coulombs  of 
electricity,  while  £  of  an  equivalent  passes  through  the  sections 
in  the  opposite  direction,  carrying  \  of  96,540  coulombs.  As  be- 
fore, in  total,  1  equivalent  of  ions  passes  through  the  middle 
section,  carrying  96,540  coulombs  of  electricity.  The  concentration 
of  the  solution  in  this  section  remains  constant,  while  that  of 
the  solution  in  the  anode  and  cathode  sections  changes.  The  solu- 
tion in  the  cathode  section  has  lost  by  separation  at  the  cathode  in 
gaseous  state  1  equivalent  of  hydrogen  ions,  and  by  migration  to 
the  anode  section,  \  of  an  equivalent  of  chlorine  ions,  and  has  gained 
£  of  an  equivalent  of  hydrogen  ions  by  migration  from  the  anode 
section.  Consequently  the  concentration  in  the  cathode  section  has 
been  decreased  by  \  of  an  equivalent  of  hydrochloric  acid,  and  is, 
therefore,  after  the  electrolysis,  equal  to  9f  equivalents.  The  solu- 
tion in  the  anode  section  has  lost,  by  separation  at  the  anode,  1 
equivalent  of  chlorine  ions,  and  by  migration  to  the  cathode  section, 


THE  MIGRATION  OF  IONS 


69 


-§-  of  an  equivalent  of  hydrogen  ions,  and  has  gained,  by  migration 
from  the  cathode,  £  of  an  equivalent  of  chlorine  ions.  It  has  then 
suffered  a  loss  of  f  of  an  equivalent  both  of  hydrogen  and  of  chlor- 
ine ions,  and  hence  its  concentration  has  fallen  to  9£  equivalents  of 
hydrochloric  acid. 

[The  foregoing  may  be  restated  briefly  as  follows :  — 

Original  concentration  in  each  section  =  10  equivalents  H"  CP. 
Concentration  in  middle  section  remains  constant. 


• 

ANODE  SECTION 

CATHODE  SECTION 

Eq.  H" 

Eq.  Cl" 

j 

Eq.  H' 

Eq.  01' 

Loss  by  separation 
Loss  by  migration 
Gain  by  migration 

Total  loss 

1 

1 
I 

1 

1 

* 

* 

1 

i 

i 

Final  concentration  H'  Cl'  9£  9$ 

To  summarize,  after  96,540  coulombs  of  electricity  have  passed 
through  the  solution,  it  is  found  that  that  part  of  it  contained  in 
the  cathode  section  has  suffered  a  change  in  concentration  from  10 
to  9f  equivalents,  or  a  loss  of  %  of  an  equivalent  of  hydrochloric 
acid,  and  that  part  contained  in  the  anode  section  a  change  from 
10  to  9£  equivalents,  or  a  loss  of  £  of  an  equivalent  of  hydrochloric 
acid.  Here,  as  was  found  in  the  diagrammatic  illustration  of  the 
electrolysis  of  hydrochloric  acid,  the  loss  in  the  cathode  section  is  to 
the  loss  in  the  anode  section  as  the  velocity  of  the  anion  is  to  the 
velocity  of  the  cation.]  In  this  case  of  hydrochloric  acid  this  ratio 
is  1 : 5.  This  may  also  be  expressed  as  follows :  — 

Loss  in  the  cathode  section  _  Velocity  of  anion  (Clf)  _  1  ,»      Trnn 
Loss  in  the  anode  section        Velocity  of  cation  (H')     5 

It  was  in  the  manner  just  indicated  that  Hittorf  was  able  to 
determine  the  relative  velocities  of  migration  of  the  different  ions 
from  the  changes  taking  place  in  the  concentration  of  the  solution 
near  the  electrodes.  His  conclusions,  although  at  first  opposed,  are 
now  generally  accepted. 

From  a  superficial  consideration  of  the  theory  of  the  independent 
migrations  of  the  ions,  it  seems  evident  that  if  one  ion  migrates 
with  a  greater  velocity  than  the  other,  an  accumulation  of  anions 


70  A  TEXT-BOOK  OF   ELECTRO-CHEMISTRY 

around  one  electrode  and  of  cations  around  the  other  must  result 
during  electrolysis.  That  this  is  not  the  case  has,  however,  already 
been  demonstrated.  A  further  question  which  naturally  presents 
itself  is:  How  can  1  equivalent  of  chlorine  separate  at  the  anode, 
when  only  ^  of  an  equivalent  is  brought  into  the  anode  section 
by  migration  ?  This  is  answered  by  assuming  that  there  is  always 
a  large  excess  of  ions  in  the  immediate  vicinity  of  the  elec- 
trode, so  that  in  any  given  time  more  ions  may  separate  on  the 
electrode  than  reach  it  by  migration.  This  action  is  assisted  by  or- 
dinary liquid  diffusion. 

The  ratio  of  the  migration  velocities  of  any  two  ions  may  be 
determined  in  a  very  simple  manner  by  the  method  indicated  in  the 
above  illustrative  problem.  It  is  only  necessary  to  divide  the  solu- 
tion of  known  concentration  into  three  parts,  as  shown  in  Figure  25, 
and,  after  the  passage  of  a  known  quantity  of  electricity  through  it, 
to  determine  the  concentration  changes  which  have  taken  place  in 
each  part.  The  concentration  of  the  middle  portion  must  remain 
constant.  If  this  is  not  the  case,  it  'shows  that  the  portions  of  so- 
lution about  the  electrodes  have  diffused  into  this  section,  thus 
destroying  the  value  of  the  determination.  Such  a  change  in  the 
concentration  of  the  middle  portion  often  takes  place  when  the  elec- 
trolysis is  too  long  continued. 

In  general,  the  quantity  of  the  substance  migrated  or  transferred, 
and  not  the  quantities  "  lost  "  about  the  electrodes,  is  used  in  calcu- 
lations. If  one  equivalent  of  the  anion  and  one  of  the  cation  is 
separated  at  the  electrodes,  and  if  the  fraction  of  an  equivalent  na  of 
the  anion  is  transferred  from  the  cathode  to  the  anode  section,  then 
the  fraction  1  —  na  of  the  cation  must  have  migrated  from  the  anode 
to  the  cathode  section.  These  experimentally  determinable  quanti- 
ties, na  and  1  —  na  (or  wc),  are  called  the  transference  numbers  of  the 
anion  and  cation,  respectively,  and  their  ratio  is  equal  to  the  ratio  of 
the  velocities  of  migration  of  the  ions.  This  is  expressed  by  the 
equation 

na     _  Velocity  of  the  anion  (ug)  __  Loss  at  the  anode  (La) 
1  —  na     Velocity  of  the  cation  (uc)      Loss  at  the  cathode  (Lc) 

From  this  equation  it  follows  that 

na  =  —  ^—  ,  andl-na  =  —  ^  — 

' 


Thus  it  is  evident  that  na  and  1  —  na  are  equal  to  the  ratios  of  the 
migration  velocity  of  the  anion  and  cation,  respectively,  to  the  sum 


THE  MIGRATION  OF  IONS  71 

of  the  two  migration  velocities.  Because  of  this  relation  na  is  also 
called  the  relative  migration  velocity  of  the  anion,  and  1  —  na  that  of 
the  cation. 

Up  to  the  present,  only  univalent  ions  have  been  taken  into 
consideration.  However,  the  transference  numbers  of  di-  or  polyva- 
lent ions  may  be  determined  in  an  analogous  manner.  If  we  con- 
sider, for  instance,  a  divalent  ion  which  is  associated  with  two 

d' 

oppositely  charged  univalent  ions,  as  in  the  case  of  Ba '       f,  then 

•    n"     represents  the  ratio  of  the  migration  velocity  of  both  chlorine 

ions  to  that  of  the  barium  ion. 

Although  the  relative  migration  velocities,  and  therefore  also  the 
ratio  of  the  migration  velocities,  can  thus  be  determined,  the  abso- 
lute value  of  each  velocity  cannot  be  found  by  this  method.  (See 
the  chapter  on  the  conductance  of  electrolytes.) 

For  the  sake  of  clearness  it  should  be  remarked  at  this  point  that, 
by  the  term  mobility  or  migration  velocity  is  meant  the  velocity  with 
which  one  equivalent  of  an  ion  moves  when  acted  upon  by  a  unit 
force.  Since,  when  acted  upon  by  any  other  force,  the  velocity 
varies  with  that  force,  the  ratio  of  the  velocities  of  the  ions  pro- 
duced by  any  given  force  is  equal  to  the  ratio  of  the  migration 
velocities.  This  subject  will  be  further  considered  in  the  section 
on  the  absolute  migration  velocities  of  ions. 

In  carrying  out  a  determination  of  the  relative  migration  veloci- 
ties of  the  ions,  naturally  the  quantity  of  the  ions  separated  at  the 
electrodes  as  electrically  neutral  substances  must  be  taken  into 
account.  An  example  taken  from  Hittorf's  work  will  now  be  con- 
sidered, in  order  to  show  how  the  calculation  of  results  is  most  eas- 
ily made. 

A  four  per  cent  solution  of  silver  nitrate  was  electrolyzed  at  18.4° 
for  a  considerable  time,  and  the  quantity  of  silver  deposited  and  the 
change  in  concentration  about  the  cathode  determined :  — 

Quantity  of  silver  deposited  and  thus  removed  from 

the  solution  about  the  cathode          .        .        .  =0.3208  gram. 
Quantity  of  silver  contained  in  a  volume  V  of  the 

solution  about  the  cathode  before  electrolysis   =  1.4751  grams. 
Quantity  of  silver  contained  in  the  same  volume 

about  the  cathode  after  electrolysis        .         .  =  1.3060  grams. 
Loss  of  silver  in  the  volume  Fof  the  solution  about 

the  cathode =  0.1691  gram. 

If  no  silver  had  come  into  this  portion  of  the  solution  about  the 


72  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

cathode  by  migration,  its  loss  would  have  been  0.3208  of  a  gram  of 
silver,  the  quantity  deposited  on  the  cathode,  instead  of  0.1691  of  a 
gram,  the  value  found.  Hence  the  quantity  of  silver  which  migrated 
to  the  cathode  portion  is  given  by  the  equation, 

0.3208  -  0.1671  =  0.1517  gram. 

If  as  much  silver  had  migrated  to  the  cathode  region  as  had  been 
removed  from  it  by  deposition  on  the  cathode,  namely,  0.3208  of  a 
gram,  then  since 

transference  number  =  q°^tity  of  the  ion  migrated, 
quantity  of  the  ion  separated 

0  8208 

transference  number  of  Ag'=    '       Q  =  l?  and 

0.3208 

transfer,  number  NO3'  =  1  —  transfer,  number  Ag'  =  0. 

This  would  show  that,  in  this  case,  the  N03'  ions  did  not  share  in 
the  migration  or  in  the  conduction  of  the  electric  current.  In  Hit- 
torf's  experiment,  then, 


transference  number  Ag'  =  =  0.473,  and 

0.3208 

transference  number  N03'  =  1  —  0.473  =  0.527. 

As  a  check  on  the  accuracy  of  the  determination,  the  change  in 
the  concentration  of  the  silver  about  the  anode  could  be  measured. 
It  should  be  found  that  the  solution  about  the  anode  has  lost  by 
migration  the  same  quantity  which  that  about  the  cathode  has 
gained.  In  the  above  experiment,  for  example,  it  should  be  found 
that  the  loss  in  silver  in  the  solution  about  the  anode,  due  to  migra- 
tion away  from  it,  is  equal  to  0.1517  of  a  gram,  which  is  identical 
with  the  gain  in  concentration  about  the  cathode  also  due  to  migra- 
tion. 

If  very  exact  results  are  desired,  it  is  advisable  to  remove  suffi- 
ciently large  portions  of  anode  and  cathode  solutions,  analyse  them, 
and  from  the  results  so  obtained,  to  calculate  the  quantities  of  the 
ions  which  have  been  transferred. 

When  the  anion  can  be  more  easily  determined  than  the  cation, 
its  concentration  changes  may  be  measured  at  the  anode,  or  the 
cathode,  or  at  both  the  anode  and  the  cathode,  quite  as  well  as  the 
concentration  change  of  the  cation.  This  may  be  illustrated  by 
the  determination  of  the  transference  numbers  of  cadmium  and  chlo- 
rine ions.  In  this  case  the  anode  consists  of  amalgamated  cadmium, 


THE  MIGRATION  OF  IONS 


73 


which  reacts  with  the  chlorine  liberated  at  its  surface,  forming 
thereby  cadmium  chloride.  Hence  the  quantity  of  chlorine  sepa- 
rated may  be  obtained  by  determining  the  loss  in  weight  of  the 
anode  during  electrolysis.  The  concentration  of  the  chlorine  about 
the  anode  before  and  after  the  passage  of  the  electric  current  is 
determined,  and  the  quantity  of  chlorine  separated  at  the  anode 
deducted  from  the  latter  value.  The  difference  obtained  by  sub- 
tracting from  the  original  concentration  the  difference  between  the 
final  concentration  and  the  quantity  of  separated  chlorine  is  the 
"  loss  "  suffered  by  the  anode  portion.  From  the  total  quantity  of 
chlorine  separated  and  from  the  loss  suffered  by  the  anode  portion, 
the  quantity  of  chlorine  which  migrated  is  easily  calculated,  since  it 
is  equal  to  the  quantity  of  chlorine  separated  diminished  by  the  loss 
about  the  anode. 

There  are  a  great  many  forms  of  apparatus  which  have  been  used 
for  the  measurement  of  transference  numbers.     In  order  to  give  an 
idea  of  the  essential  features  of  such 
an  apparatus,  that  used  by  Nernst 
and  Loeb1  for  the  determination  of 
the  transference  numbers  of  the  sil- 
ver salts  is  here  described.     It  is 
shown  in  Figure  26.     In  form  it  re- 
sembles a  Gay-Lussac  burette. 

The  two  electrodes  are  of  silver. 
When  a  current  of  electricity  is 
passed  through  the  solution,  a  quan- 
tity of  silver  deposits  upon  the  cath- 
ode (7,  which  is  a  measure  of  the 
quantity  of  electricity  passed,  and 
the  same  quantity  of  silver  dissolves 
from  the  anode  A.  In  order  to  avoid 
the  disturbance  caused  by  the  falling 
of  the  silver  from  the  cathode,  the 
latter  is  placed  in  a  side  tube,  of  the 
same  diameter  as  the  main  tube,  be- 
ing introduced  as  shown  in  the  figure. 
The  cathode  consists  of  a  cylindrical 
piece  of  silver  foil  attached  to  a 

silver  wire.     The  anode  A,  consisting  of  a  silver  wire  twisted  into 

a  spiral  at  its  lower  end  and  encased  by  a  glass  tube  throughout  its 

straight  portion,  is  placed  in  the  main  tube  as  shown.     The  openings 

1  Ztschr.  phys.  Chem.,  2,  948  (1888). 


74  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

at  a  and  c  are  closed  by  cork  stoppers  through  which  small  pieces 
of  glass  tubes  are  passed.  The  piece  of  tubing  in  a  simply  allows 
the  passage  of  the  anode  wire,  while  that  in  c  has  a  piece  of  plati- 
num wire  fused  into  its  side,  upon  which  the  cathode  hangs.  Both 
tubes  may  then  be  closed  by  means  of  pieces  of  rubber  tubing  and 
pinchcocks.  With  this  arrangement  it  is  possible  to  remove  por- 
tions of  the  solution  from  the  apparatus,  without  disturbing  the 
electrodes,  by  merely  blowing  at  the  tube  which  passes  through  c. 

In  carrying  out  an  experiment  by  means  of  this  apparatus,  the 
electrodes  together  with  the  corks,  without,  however,  the  piece  of 
rubber  tubing,  are  weighed.  When  the  apparatus  is  again  assembled 
as  shown  in  the  figure,  with  the  rubber  tube  at  a  closed  with  pinch- 
cocks,  and  the  end  of  the  tube  B  placed  in  the  solution  to  be  inves- 
tigated, it  is  filled  to  a  point  above  the  level  of  the  upper  side  of 
the  side  tube  by  sucking  at  the  rubber  tube  at  c.  The  apparatus 
usually  holds  from  forty  to  sixty  cubic  centimeters.  With  the  exit 
tube  B  closed  with  a  rubber  cap,  the  whole  apparatus  is  placed  in 
an  upright  position  in  a  thermostat.  After  the  solution  in  the 
apparatus  has  reached  the  temperature  of  the  thermostat,  the  elec- 
tric current  is  conducted  through  the  solution.  Immediately  at  the 
end  of  the  electrolysis,  the  exit  is  opened  and,  by -blowing  at  the 
tube  c,  the  desired  quantity  of  the  solution  about  the  anode  (from 
b  to  d)  is  forced  out  through  the  tube  B  into  a  tared  flask,  weighed 
and  analyzed.  The  quantity  of  solution  remaining  in  the  apparatus 
is  found  by  weighing  the  apparatus  and  liquid  together,  and  then 
subtracting  from  this  weight  the  weight  of  the  apparatus  alone.  If 
no  considerable  mixing  of  the  solution  by  diffusion  or  convection 
currents  has  occurred  during  the  electrolysis,  the  portion  of  the 
solution  about  the  anode  which  has  undergone  a  change  in  concen- 
tration is  mostly  removed  with  the  first  few  cubic  centimeters. 
The  remainder  is  thoroughly  washed  out  by  the  unchanged  solution 
which  follows  it  through  the  tube  B.  The  following  portion  of  solu- 
tion, from  d  to  e,  should  then  be  unchanged  in  concentration,  while 
the  concentration  of  the  solution  remaining  in  the  apparatus  is 
changed,  since  it  is  from  the  region  about  the  cathode.  A  test  of 
the  accuracy  of  the  experiment  is  found  in  the  unaltered  condition 
of  the  middle  portion  of  the  solution  d  e,  and  also  in  the  fact  that 
the  solution  about  the  cathode  loses  as  much  silver  as  that  about 
the  anode  gains. 

In  order  to  guard  against  a  mixing  of  the  solution,  many  investi- 
gators have  used  diaphragms.  It  is  now  known  that,  while  porous 
porcelain  membranes  may  be  used  without  thereby  incurring  error, 


THE  MIGRATION  OF  IONS  75 

other  membranes,  such  as  animal  membranes,  influence  the  value  oi 
the  transference  number.  In  the  case  of  the  latter  class,  concentra- 
tion changes  take  place  directly  at  the  two  surfaces  of  the  membrane, 
just  as  they  would  if,  in  place  of  the  membrane  or  diaphragm,  a  layer 
of  a  solvent,  in  which  the  transference  numbers  of  the  electrolyte 
are  not  the  same  as  they  are  in  the  solution,  is  introduced  into  the 
circuit. 

At  the  beginning  of  his  work,  Hittorf  questioned  himself  as  to 
the  constancy  of  transference  numbers,  and  further,  if  they  are  not 
constant,  as  to  the  circumstances  upon  which  their  variation  depends. 
Upon  further  consideration,  he  recognized  three  influences  which 
must  be  taken  into  account,  namely,  that  of  the  current,  that  of  the 
concentration  of  the  solution,  and  that  of  the  temperature.  He 
found  that  the  velocities  of  migration  were  independent  of  the 
current  and  therefore  of  the  electrical  force  acting  upon  the  ions, 
but  dependent  upon  the  concentration  of  the  solution. 

As  solutions  of  greater  and  greater  dilutions  were  examined,  he 
found  that  a  point  was  finally  reached  beyond  which  further  dilu- 
tions caused  no  appreciable  change  in  the  relative  velocities  of 
migration.  This  behavior  is  easily  explained.  In  the  concentrated 
solutions  there  are  a  large  number  of  undissociated  molecules,  which 
offer  a  resistance  to  the  motion  of  the  ions  among  them  which 
depends  upon  the  nature  of  the  molecules  and  of  the  ions.  As  the 
dilution  becomes  greater,  this  influence  gradually  disappears,  due  to 
an  increase  in  dissociation  and  to  an  increase  in  the  distance  between 
the  molecules,  and  a  consequent  decrease  in  the  resistance  offered 
by  them  to  the  motion  of  the  ions.  This  statement  may  be  applied 
to  mixtures  of  electrolytes.  In  this  case-  also  the  transference  num- 
bers of  individual  ions  remain  unchanged  for  moderate  concentra- 
tions. 

Very  exact  measurements  of  the  influence  of  concentration  on 
the  transference  number  have  recently  been  carried  out  by  A.  A. 
Noyes,1  which  show  that  for  all  the  electrolytes  investigated,  namely, 

KC1  HN03  K2S04 

NaCl          AgN03          CuS04 
HC1  Ba(N03)2 

the  transference  numbers  remain  constant  within  one  per  cent 
between  the  concentrations  0.02  and  0.1  normal.  Deviations  were 
only  observed  in  the  case  of  LiCl,  CdS04,  and  the  halogen  salts  of 
the  divalent  metals.  These  deviations  may,  as  will  be  made  evident 

1  Technology  Quarterly,  17,  No.  4,  December,  1904. 


76  A   TEXT-BOOK   OF  ELECTRO-CHEMISTRY 

later,  be  explained  on  the  assumption  of  the  formation  of  double 
molecules. 

Hittorf  did  not  discover  any  effect  produced  by  such  moderate 
changes  in  temperature  as  were  involved  in  his  work.  Recently, 
however,  Kohlrausch1  has  found  that  in  the  case  of  electrolytes 
with  monatomic  univalent  ions  the  transference  numbers  approach 
the  value  0.50  with  increasing  temperature.  It  should  be  stated 
here  that  at  the  same  time  the  difference  in  mobility  of  the  two  ions 
does  not  decrease,  but  actually  increases.  A  numerical  example 
will  make  these  statements  clear.  Consider  that,  at  the  tempera- 
ture x,  the  migration  velocity  of  the  positive  ion  is  100,  and  that  of 
the  negative  ion  is  50 ;  while  at  a  higher  temperature  y  the  velocities 
have  become  115  and  60  respectively.  The  transference  number  of 
the  positive  ion  has  increased  from  0.333  to  0.343.  It  is  evident 
that  the  value  0.50  for  the  transference  numbers  of  the  two  ions  is 
being  approached.  At  the  same  time,  however,  the  difference  be- 
tween the  single  velocities, 

100  —  50  =  50,  at  the  temperature  x, 
and  115  —  60  =  55,  at  the  temperature  y, 

has  increased  with  rising  temperature.  Such  a  simple  relation 
between  the  temperature  and  the  velocity  of  migration  of  the  ions  is 
not  found  in  the  case  of  other  classes  of  electrolytes. 

The  values  of  the  transference  numbers  obtained  with  the  solvent 
water  do  not  apply  to  other  solvents.  For  example,  while  potas- 
sium chloride,  bromide,  and  iodide  dissolved  in  water  solution  all 
give  the  value  of  the  transference  number  na  =  0.51,  when  dissolved 
in  phenol  they  all  give  the  value  of  na  =  0.19.  With  this  change  in 
the  value  of  the  transference  numbers,  there  is  a  corresponding 
change  in  concentration  at  the  boundary  surface  between  the  two 
solvents  in  which  the  same  electrolyte  is  dissolved  when  an  electric 
current  passes.2 

Still  another  advance  was  made  possible  by  Hittorf's  study  of  the 
concentration  changes  at  the  electrodes,  namely,  the  discovery  of 
the  composition  of  the  ions  resulting  from  the  dissociation  of  com- 
pounds. Silver  cyanide,  for  example,  dissolves  in  potassium  cyanide, 

1  Sitzungsber.  d.  konigl.  Pr.  Akademie  d.  Wiss.  Physik.  Mathem.  Kl.,  26,  572 
(1902). 

2Nernst  and  Riesenfeld,  Drud.  Ann.,  8,  600  and  609  (1902).  For  transfer- 
ence numbers  in  mixed  solvents  see  Jones  and  Basset,  Chem.  CentrbL,  1905,  I, 
71.  A  collection  of  references  to  the  literature  is  given  by  Walden,  Ztschr. 
phys.  Chem.,  46,  103  (1902). 


THE  MIGRATION  OF  IONS  77 

forming  a  compound  which  in  the  solid  state  has  the  composition 
represented  by  the  formula  AgCN  •  KCN.  From  this  fact  alone, 
however,  it  is  not  possible  to  state  what  ions  this  compound  forms 
upon  dissociation  in  aqueous  solution.  Now  Hittorf  passed  an 
electric  current  through  such  a  solution  and  found  that  silver  was 
deposited  upon  the  cathode.  He  determined  further  the  concen- 
tration of  potassium  and  of  silver  about  the  cathode  before  and  after 
the  electrolysis,  and  found  that,  including  the  silver  deposit,  an  in- 
crease in  the  potassium  concentration  above  that  of  the  silver  had 
taken  place,  corresponding  to  the  quantity  of  electricity  passed 
through  the  solution.  These  results  contradict  the  assumption  that 
both  the  silver  and  potassium  are  present  in  solution  as  positive 
ions.  Hittorf  interpreted  the  results  in  the  following  manner: 
The  potassium  forms  positive  ions,  while  the  silver  and  the  cyanide 
radical  unite  and  form  negative  ions.  In  solution,  then,  this  salt 
would  be  represented  by  the  formula  K*Ag(CN)2'.  Leaving  out  of 
account  the  quantity  of  separated  substance,  the  positive  and  nega- 
tive ions  must  always  be  present  in  equivalent  amounts,  which 
evidently  requires  that  before  the  electrolysis  has  taken  place  the 
solution  contain  equivalent  quantities  of  potassium  and  silver. 
The  potassium  separated  at  the  cathode  immediately  reacts  with 
water,  forming  potassium  hydroxide,  thus  explaining  the  presence  of 
an  extra  quantity  of  potassium  about  the  cathode  corresponding 
to  the  quantity  of  electricity  passed  through  the  solution.  The 
separation  of  silver  is  then  a  secondary  reaction,  caused  by  the 
action  of  the  separated  potassium,  and  resulting  in  the  appearance 
of  a  double  quantity  of  CN'  ions  in  the  place  of  decomposed 
Ag(CN)2'  ions. 

In  a  similar  manner  Hittorf  investigated  the  constitution  of  other 
double  salts  in  aqueous  solution.  He  found  that  they  dissociate  as 
shown  in  the  following  table :  — 

SYMBOL  OF  SOLID  SALT  IONS  IN  AQUEOUS  SOLUTION 

Na-jPtCle  2  Na  +  PtCl6" 

NaAuCl4  Na+AuCV 

K4Fe(CN)6  4  K'  +  Fe(CN)6"" 

K3Fe(CN)6  3  K*  +  Fe(CN)6'" 


It  is  even  more  simple  to  determine  whether  a  given  metal  exists 
in  the  positive  or  in  the  negative  ion  by  a  study  of  the  concentra- 
tion changes  which  take  place  about  the  anode  during  electrolysis. 
Since  at  this  electrode  no  deposition  of  a  metal  takes  place,  then,  if 
the  anion  is  not  decomposed  at  the  electrode,  the  solution  about  it 


78  A   TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

will  become  more  concentrated  in  respect  to  this  ion.  If  the  metal 
in  question  is  a  part  of  the  anion,  the  solution  about  the  anode  will, 
evidently,  become  more  concentrated  in  respect  to  it  also.  On  the 
other  hand,  if  it  forms  the  cation,  it  will  migrate  away  from  the 
anode,  thus  decreasing  its  concentration  in  the  solution  about  this 
electrode.  Strictly  speaking,  when  a  metal  does  form  a  part  of  an 
anion,  a  certain  quantity  of  the  metal,  even  though  it  be  an  ex- 
tremely small  part,  exists  in  solution  in  the  form  of  cations.  It 
can  happen,  moreover,  that  the  concentration  of  the  solution  about 
the  anode  does  not  undergo  a  change  in  respect  to  the  metal  during 
electrolysis.  This  is  the  case  when  the  change  in  concentration  due 
to  the  migration  of  some  of  the  metal  as  a  part  of  the  anion  is 
exactly  compensated  by  the  migration  of  the  rest  of  it  as  the  cation 
in  the  opposite  direction. 

The  constitution  of  salts  which  form  more  than  two  ions  in 
aqueous  solution  may  also  be  determined  by  means  of  transference 
numbers.1  For  example,  barium  chloride  may  dissociate  in  two 
stages  according  to  the  following  equations  :  — 


If  it  is  assumed,  accordingly,  that,  in  moderately  concentrated  solu- 
tions, the  intermediate  complex  ion  Bad*  exists,  which  on  further 
dilution  breaks  down,  then  the  transference  numbers,  which  are  ob- 
tained from  a  series  of  solutions  of  different  concentrations,  will  differ 
considerably  from  one  another.  With  increasing  dilution,  the  value 
of  the  transference  numbers  should  decrease,  since  then  the  quantity 
of  chlorine  carried  along  with  the  barium  in  the  ion  BaCl*  to  the 
cathode  is  decreased,  and  since  this  carrying  along  of  chlorine  tends 
to  increase  the  transference  number  of  the  barium  and  to  decrease 
that  of  the  chlorine.  As  a  matter  of  fact,  however,  it  was  found  that 
the  transference  numbers  varied  in  the  opposite  direction  from  that 
expected  on  the  above  assumption.  Therefore  it  is  concluded  that  in 
moderately  concentrated  solutions,  one  or  more  mols  of  undissociated 
BaCl2  combine  with  Cl',  forming  such  complex  ions  as  BaCl3f  or 
BaCl  4",  which  on  further  dilution  break  down  again.  Whether  or 
not  the  dissociation  in  stages  also  takes  place  is  not  known. 

It  has  been  suggested  by  Nernst2  that  it  would  be  possible  to 
obtain  light  on  the  question  of  hydrated  ions  by  means  of  migra- 
tion experiments.  For  instance,  if  the  positive  ion  migrates  with  a 

1  A.  A.  Noyes,  Ztschr.  phys.  Chem.,  36,  63  (1901). 

2  Jahrb.  d.  Elektrochemie,  7,  70  (1901). 


THE  MIGRATION  OF  IONS  79 

certain  number  of  water  molecules  while  the  negative  ion  migrates 
with  a  different  number,  then  during  the  electrolysis  water  is  trans- 
ferred from  one  electrode  to  the  other,  causing  a  corresponding  change 
in  concentration  of  an  indifferent,  non-conducting  dissolved  sub- 
stance, the  so-called  indicator.  As  is  evident,  this  method  gives  only 
the  difference  of  the  quantities  of  water  carried  by  the  two  ions. 
The  preliminary  results  obtained  thus  far  indicate  that  the  anions  of 
strong  mineral  acids  are  hydrated. 

Exact  experiments  with  a  solution  of  silver  nitrate  in  aqueous 
methyl  alcohol  have  recently  been  made  by  Lobry  de  Bruyn. l  He 
was  unable  to  detect  a  change  in  the  concentration  of  the  water  or 
alcohol,  and  consequently  was  unable  to  show  either  the  formation  of 
ion-hydrates  or  of  ion-alcoholates.  Morgan  and  Kanolt,2  however, 
found  that  during  the  electrolysis  of  a  solution  of  silver  nitrate  in 
water  and  pyridine  a  decrease  in  the  concentration  of  the  pyridine 
took  place  about  the  anode.  From  this  it  would  be  concluded  that 
the  pyridine  combines  with  the  silver  ions. 

The  interpretation  of  his  results  given  by  Hittorf  when  first 
published  met  with  great  opposition,  but  are  now  accepted  as  cor- 
rect. They  are  also  now  confirmed  by  the  independent  results  ob- 
tained by  determinations  of  the  freezing-point  lowering  of  solutions. 

It  is  very  interesting  to  note  that  there  are  substances,  the  so-called 
amphoteric  electrolytes,*  which  may  dissociate  in  different  ways. 
Lead  hydroxide,  Pb(OH)2,  for  example,  may  dissociate  as  follows: — 

Pb(OH)2  =  PbOH*  +  OH ' ; 
Pb(OH)2  =  Pb"     +2  OH'; 
Pb(OH)2  =  H'         +  PbO(OH) '; 
or  finally,  Pb(OH)2  =  2  H'      +  PbO  2 . 

In  pure  water  all  of  these  ions  exist  together  in  greater  or  less 
quantities  according  ]bo  the  respective  degrees  of  dissociation.  If  the 
first  two  modes  of  dissociation  predominate,  the  solution  reacts  alka- 
line ;  if  the  latter  two,  it  reacts  acid.  If  a  strong  acid  be  added  to 
the  solution,  nearly  all  of  the  OH  ions  combine  with  the  H  ions  of  the 
acid,  forming  undissociated  water.  The  reestablishment  of  the  equi- 
librium then  requires  the  further  dissociation  of  the  undissociated  or 
solid  hydroxide  into  Pb ' '  and  2  OH '.  As  before,  the  OH  ions  are 
removed  by  the  action  of  the  added  acid  and  the  end  condition  is 

1  Jahrb.  d.  Elektrochemie,  10,  260  (1904). 

2  Ztschr.  phys.  Chem.,  48,  365  (1904). 

8  Bredig,  Ztschr.  Elektrochem.,  6,  33  (1899)  ;  Ztschr.  anorg.  Chem.,  34,  202 
(1903)  ;  Walker,  Ztschr.  phys.  Chem.,  49,  82  (1904). 


80  A  TEXT-BOOK  OF   ELECTRO-CHEMISTRY 

reached  that  in  acid  solution  divalent  lead  ions  are  present  almost 
exclusively.  These  ions  may  combine  partially  with  the  anions  of 
the  acid  to  form  an  undissociated  salt,  or  they  may  form  some  such 
complex  ions  as  exist  in  the  case  of  barium  chloride. 

If  a  strong  base  be  added  to  the  solution,  the  OH  ions  remove  the 
H  ions  which  were  present,  and  we  see  at  once  that  in  an  alkaline 
solution  of  lead  hydroxide  the  Pb02  ions  will  predominate. 

The  hydroxides  of  other  metals  dissociate  similarly.  Hydroxides 
of  the  alkalies  dissociate  exclusively  into  positive  metal  ions  and 
OH  ions. 

From  what  has  been  said  it  is  evident  that  the  metal  in  solutions 
of  such  amphoteric  electrolytes  must  migrate  as  cations  to  the  cathode 
in  acid  solution  and  as  anions  to  the  anode  in  alkaline  solution. 

Lead  salts  have  been  found  to  behave  in  this  way.  To  be  sure,  the 
fact  must  also  be  taken  into  consideration  that  colloids  may  migrate 
with  or  against  the  electric  current  (see  chapter  on  electrical 
endosmose).  Hence  the  presence  of  a  metallic  oxide  as  an  anion  in 
an  alkaline  solution  is  not  conclusively  shown  by  a  migration  experi- 
ment alone. 

From  a  theoretical  standpoint  all  ions  which  are  possible  in  a 
given  solution  must  be  present.  However,  only  those  whose  existence 
may  be  detected  will  receive  consideration  here.  It  is  objectionable 
to  deal  with  ions  which  cannot  be  detected. 

There  is  a  special  class  of  amphoteric  electrolytes  which  form 
ions  which  possess  a  double  nature,  being  at  the  same  time  acid 
and  basic.  Glycocoll  furnishes  an  example  of  such  an  ion.  It  dis- 
sociates according  to  the  equilibrium  equation, 

HOH3NCH2COOH  :^-H3yCH2COOf  +  H*  +  OH'. 

The  ion  underlined  is  charged  both  positively  and  negatively,  and 
hence  is  electrically  neutral,  taking  no  part  in  migration  and  in  the 
conduction  of  the  electric  current. 

Another  experiment  concerning  the  electrolysis  of  mixtures  of 
electrolytes  which  was  performed  by  Hittorf  may  well  be  men- 
tioned here.  He  found,  in  his  study  of  solutions  of  potassium  chlo- 
ride and  of  potassium  iodide,  that  the  chlorine  and  iodine  ions 
migrate  with  very  nearly  the  same  velocity.  With  our  present 
knowledge,  it  may  be  predicted  with  great  certainty  that  during  the 
electrolysis  of  a  mixture  of  these  salts,  the  ratio  of  the  concentra- 
tions of  the  chlorine  to  that  of  the  iodine  will  not  change,  since  the 
chlorine  and  iodine  ions  take  part  equally  in  the  conduction  of  the 


THE  MIGRATION  OF  IONS  81 

electric  current.  Such  was  actually  found  to  be  the  case.  At  that 
time,  the  fact  that  when  such  a  solution  of  these  two  salts  was  elec- 
trolyzed  iodine  alone  separates  at  the  anode,  caused  much  trouble, 
since  the  phenomenon  of  electrical  conduction  was  not  distinguished 
from  that  of  electrolytic  decomposition.  It  was  concluded  that  pos- 
sibly the  iodine  alone,  belonging  to  a  more  easily  decomposed  com- 
pound, conducted  the  current.  The  fact  that  iodine  alone  separates 
at  the  anode  has  nothing  to  do  with  the  phenomenon  of  conduction. 
In  the  chapter  on  polarization  this  subject  will  be  again  considered. 

Kecently,  the  question  as  to  whether  the  lines  of  current,  or  the 
ions  migrating  from  one  electrode  to  another,  may  be  diverted  from 
their  paths  by  electro-magnetic  action,  has  received  attention,1  nega- 
tive results  being  obtained. 

Up  to  the  present  but  few  transference  experiments  have  been  car- 
ried out  with  fused  electrolytes.2 

It  is  natural  that  the  important  phenomenon  of  migration  should 
play  an  important  part  in  commercial  processes.  In  the  electrolysis 
of  concentrated  solutions  of  potassium  chloride  on  a  large  scale  in  a 
vessel  divided  into  two  parts  by  means  of  a  porous  diaphragm,  alkali 
is  produced  at  the  cathode  and  chlorine  at  the  anode.  The  latter  is 
evolved  and  collected,  while  the  alkali  accumulates  in  the  cathode 
section.  Consequently  the  alkali  thus  formed  takes  part  in  the  con- 
duction, by  the  migration  of  hydroxyl  with  the  chlorine  ions  to- 
ward the  anode,  thus  decreasing  the  yield  of  alkali.  This  decrease 
becomes  greater  the  greater  its  concentration  in  the  cathode  section. 
For  this  reason  in  the  works  the  concentration  of  alkali  is  not 
allowed  to  exceed  six  or  eight  per  cent.  It  should  especially  be 
remarked  that,  with  an  increase  in  temperature,  not  only  is  the  con- 
ductivity of  the  solution  increased,  but  also  the  yield  in  alkali  is 
increased,  since  the  transference  numbers  of  electrolytes  having 
univalent  ions  thereby  approach  the  value  0.5. 

It  seemed  surprising,  at  first,  that  the  alkali  yield  in  the  electroly- 
sis of  a  potassium  chloride  solution  is  about  ten  per  cent  higher 
than  that  in  the  electrolysis  of  a  sodium  chloride  solution  under  the 
same  conditions.  A  consideration  of  the  transference  numbers  in 
the  two  cases,  however,  explains  the  phenomenon.  The  transfer- 
ence number  of  OH' at  18°  in  1  / 1  normal  solution  of  potassium 
hydroxide  is  0.74,  while  in  a  1/1  normal  solution  of  sodium  hydrox- 
ide it  is  0.825.  Thus,  in  the  former  solution  fewer  OH  ions  migrate 
toward  the  anode  when  a  given  quantity  of  alkali  is  formed  at  the 

1  Heilbrun,  Drud.  Ann.,  15,  988  (1904). 

2  Lorenz  and  Fausti,  Ztschr.  Elektrochem.,  10,  620  (1904). 

G 


82  A  TEXT-BOOK  OF   ELECTRO-CHEMISTRY 

cathode  than  in  the  latter  solution,  since  the  migration  velocity  of 
the  potassium  ion  is  greater  than  that  of  the  sodium  ion.  The 
yield  may  also  be  increased  by  conducting  a  stream  of  carbon  diox- 
ide through  the  alkali  at  the  cathode.  The  rapid  ion  OH'  is 
thereby  replaced  by  the  slower  ion  C03".  To  be  sure,  it  must  in 
this  case  also  be  recognized  that  the  product  obtained,  the  carbon- 
ate, is  of  less  value  than  the  hydroxide. 

If  a  current  of  the  solution  is  made  to  -flow,  with  the  velocity  with 
which  the  hydroxide  ions  migrate,  from  the  anode  to  the  cathode, 
the  loss  in  alkali  is  decreased.  In  the  production  of  alkali,  it  is  only 
necessary  to  have  a  conveniently  formed  apparatus,  without  a  dia- 
phragm, through  which  a  salt  solution  may  be  allowed  to  flow  from 
the  anode  to  the  cathode,  in  order  to  obtain  a  quantitative  yield. 
Since,  however,  the  migration  velocity  of  the  OH  ions  is  consider- 
able, it  would  be  expected  that  only  a  dilute  solution  of  alkali  could 
be  obtained  when  the  electric  current  is  well  utilized.  Nevertheless, 
it  is  possible  to  obtain  a  fifteen  per  cent  solution  of  alkali  with  a 
ninety  per  cent  utilization  of  the  electric  current,  in  this  way.  The 
chief  cause  of  this  good  yield  must  be  sought  in  another  direction. 
It  is  found  in  the  stream  of  concentrated  salt  solution  which  is 
allowed  to  flow  into  the  apparatus  at  the  anode.  The  OH  ions, 
migrating  toward  the  anode,  then  pass  from  layers  of  solution  which 
are  dilute  in  respect  to  the  Cl  ions  to  those  which  are  concentrated, 
and,  consequently,  take  part  less  and  less  in  the  conduction  of  the 
electric  current.  The  progress  of  the  OH  ions  toward  the  anode  is, 
in  this  way,  checked  more  and  more  as  the  anode  is  neared.  The 
so-called  bell  process  is  based  upon  these  principles.1 

A  yield  of  alkali  which  is  almost  quantitative  may  also  be  ob- 
tained by  the  electrolysis  of  chloride  solutions,  using  a  mercury 
cathode.  In  this  way  the  formation  of  OH  ions  is  prevented,  since 
under  the  influence  of  the  electric  current  an  alkali  amalgam  is 
formed.  Care  must,  of  course,  be  taken  to  constantly  replace  the 
amalgam  with  pure  mercury.  The  former  is  transferred  to  a  second 
vessel  containing  water,  where  it  is  decomposed,  forming  alkali  and 
mercury.  This  so-called  mercury  process  is  carried  out  in  various 
modified  forms.2  It  possesses  the  advantage  that  by  means  of  it 
very  concentrated  lye,  which  is  free  from  salt  and  which  can  be  used 
directly  in  the  industries,  is  produced.  The  lye  obtained  by  the 

1  Adolph,  Ztschr.  Elektrochem.,  7,  581  (1901)  ;  Steiner,  Ztschr.  Elektrochem. , 
10,  317  (1904). 

2  F.  Glaser,  Ztschr.  Elektrochem.,  8,  522  (1902);   Kettembeil-Carrier,  Ztschr. 
Elektrochem.,  10,  561  (1908)  ;    Le  Blanc-Cantoni,  Ztschr.  Elektrochem.,  11,  60& 
H905). 


THE  MIGRATION  OF  IONS  83 

bell  or  diaphragm  processes  must  be  concentrated  by  evaporation 
and  purified  by  removing  the  salts  before  being  used. 

In  many  cases  it  is  possible  to  avoid  the  damaging  effects  of  mi- 
gration in  a  more  rational  manner.  In  the  dye  works,  a  solution  of 
chromic  acid  in  sulfuric  acid  is  generally  used  as  an  oxidizing 
agent.  During  the  oxidation,  the  chromic  acid  is  transformed  into 
chromium  sulfate.  The  chromic  acid  can  then  be  regenerated, 
electrolytically,  by  placing  the  chromium  sulfate  solution  in  the 
anode  section  of  an  electrolytic  cell,  which  is  provided  with  a  dia- 
phragm, and  sulfuric  acid  in  the  cathode  section,  and  passing  an 
electric  current  through  the  cell.  During  the  electrolysis,  SO4  ions 
migrate  from  the  cathode  section  into  the  anode  section,  thereby 
enriching  the  sulfuric  acid  in  the  latter  section  at  the  expense  of  the 
acid  in  the  cathode  section.  In  such  a  process  it  is  necessary  to 
precipitate  the  excess  of  sulfuric  acid  in  the  chromic  acid  solution 
from  time  to  time  with  lime,  and  to  replace,  with  concentrated  sul- 
furic acid,  the  diluted  and  impure  acid  of  the  cathode  section.  This 
may,  however,  be  avoided  by  first  placing  the  chromic  acid  solution 
in  the  cathode  section,  in  place  of  the  pure  sulfuric  acid,  and  passing 
an  electric  current  long  enough  to  sufficiently  oxidize  the  correspond- 
ing liquid  in  the  anode  section.  This  anode  liquid  is  used  directly 
in  the  works,  whereby  chromium  oxide  is  again  formed,  and  is  then 
allowed  to  flow  into  the  cathode  section,  where  it  is  again  electro- 
lyzed.  The  solution  used  in  the  previous  electrolysis  in  the  cathode 
section,  is,  this  time,  used  in  the  anode  section.  Before  the  second 
electrolysis,  the  cathode  solution  is  richer  in  sulfuric  acid  than  the 
anode  solution,  but  during  it  this  excess  migrates  to  the  latter  solu- 
tion. A  cyclical  process  is  thus  carried  out,  in  which  the  chromic 
acid  solution  is  alternately  placed  in  the  anode  and  cathode  sections, 
thus  preventing  the  accumulation  of  an  excess  of  sulfuric  acid  in  it, 
and  making  it  possible  to  maintain  the  solution  at  a  given  concen- 
tration during  its  regeneration  by  electrolysis.  By  means  of  such  a 
process,  a  solution  of  chromic  acid  in  sulfuric  acid  may  be  used  as  an 
oxygen  carrier  as  long  as  desired  without  loss  of  either  chromic  or 
sulfuric  acid.1 

A  table  of  the  transference  numbers  of  the  ions  of  the  most  im- 
portant and  best-investigated  electrolytes  is  given  on  the  next 
page.  The  values  have  been  taken  from  Kohlrausch  and  Holborn's 
"Das  Leitvermogen  der  Elektrolyte,"  and  from  the  recent  works  of 
Noyes,2  Jahn,3  and  Tower.4 

1  Le  Blanc,  Ztschr.  Elektrochem.,  7,        8  Ztschr.  Phys.  Chem.,  37,  673  (1901). 
290  (1900).  *  J.  Am.  Chem.  Soc.,  26,  1039  (1904). 

2  Ztschr.  Phys.  Chem.,  36,  63  (1901). 


A   TEXT-BOOK  OF  ELECTRO-CHEMISTRY 


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CHAPTER  V 

THE    CONDUCTANCE    OP    ELECTROLYTES 

Specific  and  Equivalent  Conductance.  —  The  conception  of  resist- 
ance in  the  case  of  conductors  of  the  first  class  has  already  been 
discussed.  The  resistance  of  such  conductors  is  dependent  upon  the 
nature  of  the  material  of  which  they  are  formed,  their  form,  and 
their  temperature.  If,  for  a  cylinder  one  centimeter  in  length  and 
one  square  centimeter  in  cross  section,  of  a  certain  substance, 

K,  the  resistance  =  - , 

K 

then  for  any  cylindrical  piece  of  the  same  substance  at  the  same 
temperature, 

i-ixi 

K     s 

when  I  represents  the  length  of  the  cylinder  in  centimeters  and  s 
its  cross  section  in  square  centimeters.  The  factor  -  represents 

K. 

the  specific  resistance  of  the  substance.  It  depends  only  on  the 
temperature. 

The  unit  of  resistance  is  the  ohm.  It  is  the  resistance  of  a  con- 
ductor in  which  a  current  of  one  ampere  flows  when  a  difference  of 
potential  of  one  volt  exists  between  the  ends  of  the  conductor.  A 
substance  which  in  the  form  of  a  cylinder  one  centimeter  in  length 
and  one  square  centimeter  in  cross  section  possesses  a  resistance  of 

one  ohm  represents  a  unit  of  resistance.     For  it  -  =  1.     In  practice, 

K. 

however,  the  unit  of  resistance  is  represented  by  the  resistance  of  a 
column  of  mercury,  106.3  centimeters  in  height  and  one  square 
millimeter  in  cross  section,  at  the  temperature  of  melting  ice.  The 
mass  of  this  column  of  mercury  must  be  14.4521  grams. 

Formerly,  the  unit  of  resistance  was  defined  to  be  the  resistance 
of  a  column  of  mercury,  one  meter  in  length  and  one  square  milli- 
meter in  cross  section  at  0°  t.  This  unit  is  known  as  the  Siemens  or 
mercury  unit.  It  is  related  to  the  new  unit  as  1 : 1.063,  and  there- 

85 


86  A  TEXT-BOOK  OF   ELECTRO-CHEMISTRY 

fore,  in  order  to  calculate  the  resistance  in  ohms  from  a  resistance 
expressed  in  Siemens  units,  or  conversely,  the  following  equation 
may  be  used:  — 

Resistance  in  ohms  =  Resistance  in  Siemens  units  H-  1.063. 

In  the  following  pages,  the  ohm  is  used  as  the  unit  of  resistance. 

The  greater  the  resistance,  the  less  the  conductance ;  and,  con- 
versely, the  greater  the  conductance,  the  less  the  resistance.  Hence, 
the  resistance  B  and  the  conductance  K  are  reciprocal  quantities,  or 


The  word  conductance  is  used  mainly  with  reference  to  solutions, 
and  in  the  following  pages  will  be  used  only  with  such  a  reference. 
Just  as  in  the  case  of  conductors  of  the  first  class,  the  unit  of 
specific  conductance,  which  may  be  expressed  in  reciprocal  ohms, 
could  be  represented  by  the  conductance  of  a  cylinder  of  a  liquid, 
one  centimeter  in  height  and  one  square  centimeter  in  cross  section.,, 
which  possesses  a  resistance  of  one  ohm.  For  such  a  liquid  K  =  1, 
Furthermore,  the  same  law  which  expresses  the  variation  of  the 
resistance  of  a  conductor  at  constant  temperature  with  a  variation 
of  its  dimensions  applies  also  to  conductors  of  the  second  class. 
That  is, 

K  =  -  =  K  x  -> 

R  I 

where  K  is  the  conductance,  K  the  specific  conductance,  or  conduc- 
tivity, B  the  resistance,  s  the  cross  section,  and  I  the  length  of  the 
liquid  conductor.  This  method  of  expressing  conductance  has  not, 
however,  been  found  suitable  for  obtaining  numerical  relationships 
between  solutions.  Since  electro-chemistry  deals  chiefly  with  solu- 
tions, it  has  been  found  advisable  to  adopt  a  special  method  of 
expressing  their  conductances.  In  the  case  of  solutions,  the  con- 
ductance depends  almost  entirely  upon,  the  solute,  or  the  dissolved 
substance,  and  in  comparing  their  conductances,  it  has  been  found 
advantageous  to  refer  the  conductances  to  a  certain  quantity  of 
solute,  namely,  one  equivalent  weight,  rather  than  to  any  particular 
volume  of  solution.  The  conductance  of  a  solution  containing  one 
equivalent  of  the  solute,  when  placed  between  parallel  electrodes 
one  centimeter  apart,  is  called  its  equivalent  conductance  g. 

If  C"e  represents  the  equivalent  concentration  of  a  solution,  i.e.  the 
concentration  expressed  in  equivalents  of  the  solute  per  cubic  centi- 
meter of  solution,  then 


CONDUCTANCE   OF  ELECTROLYTES 


87 


where  D'e  represents  the  equivalent  dilution  of  the  solution,  or  in 
other  words,  the  volume  in  cubic  centimeters  which  contains  one 
equivalent  of  the  solute.  Accordingly, 


The  relation  between  the  equivalent  conductance  n  and  the  spe- 
cific conductance  K  is  reached  as  follows  :  [Consider  a  vessel,  such 
as  is  shown  in  Figure  27,  constructed  of  two  non-corrodible  metallic 
plates  A  and  C,  serving  as  electrodes,  which  are  held  at  a  distance 
of  one  centimeter  from  each  other  by  the  nonconducting  material 
which  forms  the  ends  and  bottom  of  the  vessel.] 

One  cubic  centimeter  of  a  solution  containing  one  equivalent  of  a 
solute  is  placed  in  this  vessel,  reaching  to  the  level  a.  The  cross 
section  of  the  solution,  perpendicular  to  the 
direction  of  the  electric  current  between  the 
two  electrodes,  is  then  one  square  centimeter. 
The  equivalent  concentration  of  this  solution 
is  unity,  and  hence  its  dilution  is  also  unity. 
Since  its  volume  is  one  cubic  centimeter  and 
it  is  placed  between  electrodes  one  centi- 
meter apart,  its  conductance  is  directly  the  JL, 
specific  conductance  or  conductivity,  and 
since  it  contains  one  equivalent  weight  of 
dissolved  substance  placed  between  elec- 
trodes one  centimeter  apart,  its  conductance 
is  also  the  equivalent  conductance.  These 
facts  concerning  this  solution  may  also  be 
expressed  by  the  following  equations  :  — 

C'e  =  1,  Dfe  =  1,  and  K  =K  =^. 

If,  however,  the  volume  of  the  above  solution  be  increased  to  one 
thousand  cubic  centimeters  by  the  addition  of  water,  thereby  reach- 
ing the  new  level  6,  the  cross  section  of  this  solution  is  one  thou- 
sand times  as  great  as  that  of  the  original  solution,  or  one  thousand 
square  centimeters.  But  the  conductance  of  a  quantity  of  this  solu- 
tion having  a  cross  section  of  one  square  centimeter  is  the  specific 
conductance,  or  the  conductivity  of  the  solution.  Hence  the  actual 
conductance  of  this  solution  is  one  thousand  times  as  great  as  the 
specific  conductance,  or  conductivity.  The  solution  still  contains 
one  equivalent  of  the  dissolved  substance  between  the  electrodes, 
and  therefore  the  actual  conductance  is  still  identical  with  the 


Fia.  27 


88 


A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 


equivalent  conductance,  this  time  at  the  dilution,  1000.  It  may 
be  said,  in  general,  that  whenever  one  equivalent  of  a  substance  in 
aqueous  solution,  of  any  concentration  or  dilution,  is  placed  in  such 
a  vessel,  its  actual  conductance  is  equal  to  the  equivalent  conduc- 
tance at  the  concentration  in  question.  It  follows  from  what  has 
been  stated,  that  in  the  above  case  the  equivalent  conductance  of 
the  solution  is  also  one  thousand  times  as  great  as  its  conductivity. 
These  relations  are  expressed  by  the  following  equations :  — 


The  specific  conductance,  or  conductivity,  of  a  solution  changes 
nearly  in  proportion  to  the  concentration,  while  the  equivalent  con- 
ductance generally  increases  rapidly  at  first,  then  more  slowly,  and 
finally  remains  constant,  with  decreasing  concentration.  This  will  be 
evident  from  a  study  of  the  table  of  equivalent  conductances  of  salts, 
acids,  and  bases  in  aqueous  solution  at  different  concentrations, 
given  here.  This  table  contains  among  other  results  the  most  recent 
ones  obtained  by  Kohlrausch. 

EQUIVALENT  CONDUCTANCES  AT  18°  t 


Ce 
equiva- 
lent 
concen- 
tration* 

KC1 

NaCl 

KNOs 

AgNOs 

iCuSO« 

*H2S04 

HC1 

CH,COOH 

KOH 

NH» 

D« 

equiva- 
lent 
dilution' 

0.0001 

129.07 

108.10 

125.50 

115.01 

109.95 

_ 

_ 

107 

_ 

(66) 

10000 

0.0002 

128.T7 

107.82 

125.18 

114.56 

107.90 

_ 

_ 

80 

— 

53 

5000 

0.0005 

128.11 

107.18 

124.44 

113.88 

103.56 

(868) 

— 

57 

— 

38.0 

2000 

0.001 

127.34 

106.49 

123.65 

113.14 

98.56 

861 

(877) 

41 

(234) 

28.0 

1000 

0.002 

126.31 

105.55 

122.60 

112.07 

91.94 

851 

876 

80.2 

(233) 

20.6 

500 

0.005 

124.41 

103.78 

120.47 

110.03 

80.98 

330 

878 

20.0 

230 

13.2 

200 

0.01 

122.43 

101.95 

118.19 

107.80 

71.74 

808 

370 

14.3 

228 

9.6 

100 

0.02 

119.96 

99.62 

115.21 

— 

62.40 

286 

367 

10.4 

225 

7.1 

50 

0.05 

115.75 

95.71 

109.86 

99.50 

51.16 

258 

360 

6.48 

219 

4.6 

20 

0.1 

112.03 

92.02 

104.79 

94.33 

43.85 

225 

851 

4.60 

213 

8.3 

10 

0.2 

107.96 

87.73 

98.74 

_ 

37.66 

214 

842 

8.24 

206 

2.30 

5 

0.5 

102.41 

80.94 

89.24 

77.5 

— 

205 

327 

2.01 

197 

1.35 

2 

1 

98.27 

74.35 

80.46 

67.6 

25.77 

198 

801 

1.32 

184 

0.89 

1 

2 

92.6 

64.8 

69.4 

_ 

_ 

183.0 

254 

0.80 

160.8 

0.532 

0.5 

3 

88.3 

56.5 

(61.8) 

— 

— 

166.8 

215.0 

0.54 

140.6 

0.364 

0.83 

5 

— 

42.7 

— 

— 

— 

135.0 

152.2 

0.285 

105.8 

0.202 

0.2 

1  Equivalent  concentration,  Ce  =  Eqnivalents. 

Liters 

2  Equivalent  dilution,  D«  =       Liters      . 

Equivalents 


CONDUCTANCE  OF   ELECTROLYTES 


89 


General  Regularities.  —  The  first  clear  conceptions  concerning  the 
conductance  of  electrolytes  resulted  from  the  epoch-making  work  of 
Kohlrausch.  The  work  of  discovery  was  then  rapidly  pushed  for- 
ward by  Arrhenius,  Ostwald,  and  others.  It  was  found  that,  with- 
out exception,  the  equivalent  conductance  of  different  electrolytes 
increases  with  increasing  dilution,  reaching  in  many  cases  a  maxi- 
mum value  which  does  not  change  upon  further  dilution.  The  fol- 
lowing statement,  called  Kohlrausch's  principle,1  has  been  found  to 
hold  for  solutions  which  have  been  diluted  until  the  maximum 
equivalent  conductance  has  been  reached :  — 

The  equivalent  conductance  of  a  binary  electrolyte  is  equal  to  the  sum 
of  two  valuesj  one  of  ivhich  depends  upon  the  cation,  and  the  other  upon 
the  anion. 

This  principle  expresses  the  fact  that  the  conductance  of  an  elec- 
trolyte is  equal  to  the  sum  of  the  conductances  of  its  ions.  Because 
of  this  fact  the  conductance  of  an  electrolyte  is  called  an  additive 
property.  The  principle  is  evident  from  a  study  of  the  following 
table,2  in  which  the  equivalent  conductances,  at  great  dilutions  of 
several  series  of  salts,  are  given.  For  example,  in  the  first  horizontal 
row  are  given  the  values  for  KC1,  NaCl,  T1C1,  and  LiCl,  and  the 
differences  between  these  values  ;  while  in  the  first  column  are  given 
the  equivalent  conductances  of  KCl,KN03,KF,and  KC2H302,  and  also 
the  differences  between  these  values.  The  differences  in  each  case 
are  printed  in  small  type. 


K 

diff. 

Na 

diff. 

Tl 

diff. 

Li 

Cl  . 

129  1 

21  0 

108  1 

22  2 

130  3 

82  2 

98.1 

diff.= 
N08  

8.6 
125.5 

20  9 

8.5 
104.6 

22  0 

3.7 
126.6 

821 

8.6 

94.5 

diff.= 
F  

15.0 

110.5 

21  1 

15.2 

89.4 

25  0 

12.2 

114.4 

diff.= 
C2H3O2  

10.5 
100  0 

28  2 

12.6 
76.8 

- 

- 

If  now  the  differences  in  the  rows  and  in  the  columns  be  consid- 
ered, it  is  seen  that  they  are  nearly  constant  for  any  given  row  or 
column.  Such  a  relation  is  possible  only  when  the  values  of  the  con- 
ductances are  made  up  of  two  independent  constants.  A  great  many 
other  properties  of  dilute  solutions  of  electrolytes  are  known  which 
may  similarly  be  considered  as  the  average  of  the  properties  of  the 

1  Wied.  Ann.,  6,  1  (1879),  and  26,  213  (1885). 

2  Temperature  =  18°  t ;  equivalent  dilution  =107  c.cm. 


90  A   TEXT-BOOK  OF   ELECTRO-CHEMISTRY 

ions  constituting  the  electrolyte.  Such  properties  are  called  additive 
properties.  As  further  examples  of  such  properties  of  solutions, 
may  be  mentioned  the  color  and  the  index  of  refraction. 

It  will  be  seen  that  the  dissociation  theory  offers  a  ready  explana- 
tion for  the  above  experimentally  found  regularities.  The  conduc- 
tion of  electricity  through  a  solution  consists  in  the  motion  of  single 
ions.  If,  when  a  solution  containing  x  ions  is  placed  in  an  electric 
circuit,  100  ions  pass  through  a  cross  section  of  the  solution  in  a 
given  time,  then,  if  the  number  of  ions  be  increased  to  2  x,  other 
conditions  remaining  constant,  200  ions  will  pass  through  a  cross 
section  in  the  same  time.  In  other  words,  when  the  number  of  ions 
in  a  given  solution  is  doubled,  the  conductance  of  the  solution  is  also 
doubled. 

As  has  already  been  indicated,  the  equivalent  conductance  of  a 
binary  electrolyte  can  be  measured  directly  by  placing  a  solution 
containing  one  equivalent  of  it  in  a  vessel,  such  as  is  shown  in 
Figure  27,  two  of  whose  walls  (exactly  one  centimeter  apart)  serve 
as  electrodes.  Other  dimensions  of  the  vessel  than  the  distance 
between  the  wall-electrodes  need  not  be  fixed.  The  actual  conduc- 
tance measured  is  then  the  equivalent  conductance.  As  long  as  one 
equivalent  of  the  electrolyte  is  in  solution  between  the  electrodes, 
this  is  always  the  case,  whatever  the  volume  of  the  solution  may  be. 
When  the  electrolyte  is  completely  dissociated,  its  solution  contains 
one  equivalent  of  anions  and  one  of  cations.  Its  equivalent  conduc- 
tance, then,  remains  constant,  whatever  the  dilution,  since  the  same 
number  of  ions  is  always  present,  and  since  it  is  by  means  of  these 
ions  alone  that  the  conduction  takes  place.  The  conductance  of  the 
electrolyte  is  independent  of  the  size  of  the  electrodes,  providing  a 
change  in  size  is  not  accompanied  by  either  an  increase  or  a  decrease 
in  the  number  of  ions  in  the  solution.  Hence  it  is  possible  to 
extend  the  wall-electrodes  to  any  desired  size,  without  thereby  affect- 
ing the  conductance  of  a  given  solution  placed  between  them,  and 
thus  to  measure  the  equivalent  conductance  directly  at  such  great 
dilutions  that  its  value  finally  remains  practically  constant.  From 
what  has  been  said  it  is  easy  to  understand  why  the  equivalent  con- 
ductance of  a  concentrated  solution  is  less  than  that  of  a  dilute 
solution.  In  the  former  case,  since  more  molecules  remain  undissoci- 
ate  than  in  the  latter  case,  it  follows  that  fewer  ions  per  equivalent 
of  electrolyte  are  present  to  conduct  the  electric  current.  Hence  it 
may  be  stated  — 

With  increasing  dilution  the  degree  of  dissociation,  and  consequently 
also  the  equivalent  conductance.,  of  an  electrolyte  increases,  until  complete 


CONDUCTANCE  OF   ELECTROLYTES  91 

dissociation  and  the  corresponding,  or  maximum,  value  of  the  equivalent 
conductance  is  reached. 

The  requirement  of  the  dissociation  theory  that  upon  dilution  the 
equivalent  conductance  should  increase,  reaching  a  maximum  con- 
stant value  at  great  dilutions,  is  in  complete  agreement  with  facts. 
According  to  the  Clausius  theory,  however,  the  conductivity  depends 
upon  the  frequency  of  the  changes  which  take  place  between  the 
positive  and  negative  parts  of  the  molecules.  It  is,  therefore,  a 
natural  conclusion  from  this  theory  that  the  more  concentrated  the 
solution,  the  more  often  will  these  changes  take  place,  and,  conse- 
quently, the  greater  will  be  the  equivalent  conductance.  This,  how- 
ever, is  in  direct  contradiction  to  facts.  The  superiority  of  the 
dissociation  theory  over  the  Clausius  theory  is,  in  this  case,  at  once 
evident. 

The  conductance  of  a  solution  depends  not  only  upon  the  number 
of  ions  which  exists  between  the  two  electrodes,  but  also  upon  the 
sum  of  their  velocities  of  migration.  Since  dilute  equivalent  solu- 
tions of  neutral  salts,  strong  acids,  and  strong  bases  are  practically 
completely  dissociated,  they  contain  the  same  number  of  ions,  and 
consequently  their  equivalent  conductances  are  to  each  other  as  the 
sums  of  the  •  migration  velocities  of  their  respective  ions.  Since  an 
ion  is  free  to  move  independently  of  other  ions  present  in  the  solu- 
tion, it  possesses  an  independent  and  constant  velocity  of  migration. 
It  follows  then  that  the  equivalent  conductance  may  be  expressed 
in  terms  of  the  sum  of  the  migration  velocities  of  the  ions  involved 
and  a  constant  which  depends  upon  the  units  chosen,  as  follows :  — 

K=  constant  x  (ua  +  uc), 

where  ua  and  uc  represent  the  migration  velocities  of  one  equiva- 
lent of  positive  and  negative  ions,  respectively  (see  page  70).  This 
is  an  expression  of  the  Law  of  Kohlrausch. 

The  sum  of  the  migration  velocities  may  therefore  be  obtained 
from  the  maximum  value  of  the  equivalent  conductance.  The  rela- 
tion between  the  single  migration  velocities,  or  the  relative  migra- 
tion velocity,  is  known  from  Hittorf's  work.  Therefore  the  single 
values  may  be  calculated. 

K  =  const.  (ua  +  uc) ; 

Wa==uc+ua; 
na£=  const.  X  ua, 

or  ua=  — 2=— ; 

const. 


92  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

and  (1  —  W.)K  =  const,  x  uc, 

u.=<*  -*•)». 

const. 

If  the  migration  velocities  are  expressed  in  the  same  units  as  the 
conductances,  then  the  constant  becomes  unity.  The  above  equations 
may  be  written  as  follows  :  — 

and  uc  =  (1  —  na)K. 


When  the  value  of  the  velocity  of  migration  of  a  given  ion  is 
once  determined,  that  of  the  others  may  be  calculated  either  from 
transference  numbers  or  relative  migration  velocities,  or  from  the 
maximum  values  of  the  equivalent  conductances,  whenever  these 
are  known.  Kohlrausch  has  calculated  and  compared  many  of  these 
migration  velocities  and  found  that  the  two  methods  of  determina- 
tion give  the  same  results.  This  agreement  of  results  obtained 
from  two  sources  is  a  strong  confirmation  of  the  correctness  of 
the  present  conceptions  of  electrolysis. 

The  following  illustrative  example  will  make  the  method  of  calcu- 
lation clearer. 

The  maximum  value  of  the  equivalent  conductance  K*,  or  the 
value  at  infinite  dilution,  of  potassium  chloride  was  found  by  a 
method  of  extrapolation  to  be  129.9.  The  transference  numbers  in  a 
very  dilute  solution  of  the  salt  were  found  to  be  — 

na  =  0.503        and  1  -  na  =  0.497  ; 
but                    ua  =  ^oKao,  uc  =  1  —  w0Kao, 

or  ua  =  0.503  x  129.9,  uc  =  0.697  x  129.9  ; 

u0  =  65.3,  uc  =  64.6. 

The  corresponding  equivalent  conductance  of  sodium  chloride  was 
found  to  be  108.9.  The  value  of  ua,  or  the  migration  velocity  of 
chlorine,  was  found  in  the  preceding  paragraph  to  be  65.3.  Hence, 
since 

Koo  =  U0  +  Uc, 

uc  =  108.8  —  65.3  =  43.6  for  sodium. 

The  transference  numbers  in  a  sodium  chloride  solution  were  found 
tobe  — 

na  =  0.604,  l-wa  =  0.396; 

but  n  =      Ua 


or,  since     u.  =  65.3,    uc  =  -~-     -  65.3  =  42.8  for  sodium. 


CONDUCTANCE  OF  ELECTROLYTES 


93 


These  two  values  for  the  migration  velocity  of  sodium  agree  satis- 
factorily with  each  other. 

The  following  values  of  the  migration  velocity,  at  infinite  dilution, 
at  18°  t,  are  taken  from  those  collected  by  Kohlrausch : l  — 


CATIONS 

ANIONS 

CATION 

uc 

CATIONS 

vc 

ANION 

XJa 

ANIONS 

r« 

H 

318. 

4Ba 

55.10 

OH 

174. 

CH02 

46.7 

K 

64.87 

\  Sr 

51.54 

Fl 

46.64 

C2H802 

35.0 

Na 

43.55 

i  Ca 

51.46 

Cl 

65.44 

C3H602 

31.0 

Li 

33.44 

£  Mg 

45.94 

Br 

67.63 

C4H7O2 

27.6 

Rb 

67.6 

\  Zn 

46.57 

I 

66.40 

C6H»02 

25.7 

Cs 

68.2 

i  Qd 

47.35 

SCN 

56.63 

C6HnO2 

24.3 

NH4 

64.4 

i  Cu 

47.16 

C108 

55.03 

*  (C00)2 

62.6 

Tl 

66.00 

JPb 

61.10 

Br03 

46.2 

£SO4 

68.14 

Ag 

54.02 

I03 

33.87 

\  CrO4 

72.0 

NO8 

61.78 

^  CO8 

60.0 

C104 

64.7 

I04 

47.7 

MnO4 

53.4 

Further  values  are  given  in  the  section  on  the  migration  velocity 
of  individual  ions  (see  page  116).  The  corresponding  values  for 
other  temperatures  may  be  calculated  with  the  aid  of  the  tempera- 
ture coefficient  given  later  in  this  chapter. 

The  conductance  at  great  dilution  is  expressed  by  the  equation, 

K,  =  Uc  +  UB. 

In  this  case  the  dissociation  is  complete.  If,  on  the  other  hand,  at 
any  other  dilution  D  only  a  part  of  the  molecules  is  dissociated,  then 
the  conductance  is  less.  For  example,  if  at  this  dilution  but  one  half 
of  the  total  number  of  molecules  are  dissociated,  the  conductance  is 
but  one  half  its  value  at  infinite  dilution.  This  is  expressed  by  the 
equation, 


1  Sitzungsber.  d.  K.  Pr.  Akad.  d.  Wiss.  Physik.  Math.  Kl.,  574  and  582  (1902), 
and  also  in  the  number  dated  July  28,  1904.  (Abstracted  in  Ztschr.  phys.  Chem., 
51,  744,  1905). 

The  value  for  H*  has  been  confirmed  by  the  recent  work  of  Goodwin  and 
Haskell,  Proc.  Am.  Acad.  of  Arts  and  Sci.,  Vol.  40,  No.  7  (September,  1904). 

The  value  for  CO3"  has  been  taken  from  the  investigation  of  Bottger,  Ztschr. 
phys.  Chem.,  46,  594  (1903). 

An  attempt  to  explain  the  strikingly  great  mobility  of  H*  and  OH'  has  been 
given  by  Danneel,  Ztschr.  Elektrochem.,  11,  249  (1905). 


94  A   TEXT-BOOK   OF  ELECTRO-CHEMISTRY 

In  deriving  this  equation,  it  was  tacitly  assumed  that  the  elec- 
trolytic friction,  or  the  friction  offered  by  other  dissolved  particles  or 
by  the  molecules  of  the  solvent  itself,  to  the  movement  of  the  ions 
is,  in  dilute  solutions,  independent  of  the  concentration.  This 
assumption  being  borne  in  mind,  the  equation  may  be  generalized  to 
apply  to  monovalent  or  polyvalent  ions  as  follows :  — 

Kj,  =  X   (Uc  +  U,). 

Here  K^,  represents  the  equivalent  conductance  of  the  electrolyte, 
or  the  conductance  when  one  equivalent  of  it  is  dissolved  in  D  cubic 
centimeters  of  the  solvent,  and  x  the  per  cent  of  the  equivalent 
which  is  dissociated  into  ions,  i.e.  the  degree  of  dissociation.  By 
combining  the  equations  — 

K^  =  uc  +  ua  and  KD  =  x  (uc  +  u.), 

where  K^  represents  the  maximum  value  of  the  equivalent  conduc- 
tance or  its  value  at  infinite  dilution,  the  value  of  x}  or  the  degree  of 
dissociation,  can  be  calculated. 

•-£ 

The  degree  of  dissociation  of  a  substance  in  solution  is  equal  to  the 
ratio  of  its  equivalent  conductance  in  that  solution  to  its  equivalent 
conductance  in  a  solution  of  infinite  volume. 

As  has  already  been  seen  (see  page  58),  Arrhenius  had  come  to 
this  conclusion  and  had  also  found  that  the  values  of  the  degree  of 
dissociation  obtained  from  measurements  of  the  freezing-point  lower- 
ing of  solutions  agree  satisfactorily  with  those  calculated  from  the 
electrical  conductance.  The  extent  of  this  agreement  is  well  shown 
in  the  carefully  prepared  article  of  A.  A.  Noyes.1  According  to  this 
article,  the  values  obtained  by  the  two  methods  do  not  differ  by 
more  than  two  or  three  per  cent  between  the  concentrations  0.005 
and  0.25  normal  in  the  case  of  the  salts,  —  NaCl,  KC1,  Na2S04,  K2S04, 
and  BaCl2.  It  should  also  be  mentioned  in  this  connection  that  the 
experimentally  determined  values  of  the  electromotive  force  of  con- 
centration cells  (see  the  chapter  on  electromotive  force)  do  not  differ 
more  than  about  one  per  cent  from  the  values  calculated  with  the  aid 
of  the  dissociation  values  obtained  from  conductivity  measurements. 

The  determination  of  the  degree  of  dissociation  of  different  sub- 
stances has  become  a  very  important  work. 

Ostwald  found  that  the  order  in  which  acids  accelerate  or  catalyze 

1  Technology  Quarterly,  17,  No.  4,  December,  1904. 


CONDUCTANCE   OF   ELECTROLYTES  95 

the  saponification  of  methyl  acetate,  or  invert  cane  sugar,  is  also  the 
order  in  which  they  compete  for  a  base.  The  latter  can  be  deter- 
mined by  either  thermochemical  or  volume-chemical  measurements. 
Thus  a  measure  of  the  "  strength  "  or  "  affinity  "  of  an  acid  (or  base) 
was  obtained. 

Arrhenius  sought  to  discover  the  existence  of  a  relation  between 
electrical  conductance  and  chemical  activity,  and  found  that,  in 
reality,  the  two  properties  are  closely  related.  As  in  the  case  of  the 
equivalent  conductance,  the  chemical  activity  or  strength  of  an  acid 
increases  with  the  dilution  and  finally  reaches  a  limiting  value. 
Consider,  for  instance,  two  equivalent  solutions  of  different  acids. 
If  the  degree  of  dissociation  is  different  in  the  two  cases,  then  the 
chemical  activities  or  strengths  of  the  two  acids  will  also  be  different. 
On  diluting  the  two  solutions  the  dissociation  of  each  acid  increases 
with  a  ratio  of  its  own  until,  at  great  dilutions,  it  is  complete.  At 
such  dilutions  the  two  acids  possess  equal  chemical  activities  or 
strengths.  The  relative  strengths  of  acids  and  bases  change,  there- 
fore, with  the  concentration.  This  was  shown  by  Ostwald  before  the 
rise  of  the  theory  of  electrolytic  dissociation. 

Application  of  the  Mass-action  Law  to  Gaseous  and  to  Electrolytic 
Dissociation.  —  Accepting  the  dissociation  theory,  and  the  applica- 
bility of  the  gas  laws  to  dissolved  substances,  as  established  by  van't 
Hoff,  a  dissociation  or  affinity  constant,  which  is  independent  of  the 
dilution,  may  be  calculated.  This  was  first  shown  by  Ostwald.1 

According  to  the  law  of  mass  action,  at  constant  temperature  the 
following  principle  holds  for  a  gas  which  dissociates  into  two 
components  :  — 

The  product  of  the  active  masses  of  the  two  components,  divided  by 
the  active  mass  of  the  undissociated  part,  is  a  constant. 

By  the  active  mass  of  a  substance  is  meant  the  number  of  mols 
of  it  which  are  contained  in  the  unit  volume.  It  is,  therefore,  iden- 
tical with  the  molar  concentration.  In  the  case  of  gases,  partial 
pressures,  which  are  proportional  to  the  active  masses,  may  be  sub- 
stituted for  the  active  mass  in  the  above  statement.  Consider,  for 
example,  the  dissociation  of  ammonium  chloride,  at  a  high  and 
constant  temperature,  into  hydrochloric  acid  and  ammonia  according 
to  the  equation  :  — 

NH4C1  ^±  NH3  +-  HC1. 


Then  according  to  the  law  of  mass  action, 

J>fNH8  X  J/HCI  P"  TT 

—  —  **-dl 

JPNH4C1  .PNH4C1 

*Ztschr.  phys.  Chem.,  2,  270  (1888). 


96  A   TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

where  p'NHs>  P'RCI,  and  pNH4ci  represent  the  partial  pressures  of  ammo 
nia,  hydrochloric  acid,  and  undissociated  ammonium  chloride,  respec- 
tively, and  Kd  a  constant  characteristic  of  the  equilibrium  existing 
between  these  substances  at  the  temperature  in  question  but  inde- 
pendent of  the  values  of  the  single  partial  pressures.  Thus,  at  the 
constant  temperature,  the  gaseous  mixture  may  be  compressed  or 
expanded,  or  an  excess  of  any  one  of  the  constituents  may  be  added, 
without  changing  the  value  of  the  constant  or  the  form  of  the  above 
equation.  It  is  therefore  evident  that,  whenever  these  three  gases 
are  brought  together  in  whatever  proportions  at  this  constant  tem- 
perature, such  a  rearrangement  takes  place  in  their  individual  con- 
centrations, or  partial  pressures,  that  the  above  equation  is  still 
satisfied  with  the  same  value  of  the  constant.  Thus  if  ammonia  gas 
be  added  to  a  given  volume  of  the  dissociated  ammonium  chloride,  the 
partial  pressure  of  the  ammonia  in  the  mixture  is  thereby  increased. 
In  this  case,  if  the  partial  pressures  of  the  hydrochloric  acid  and  of 
the  undissociated  ammonium  chloride  did  not  undergo  a  change,  the 
constant  Kd  would  necessarily  increase.  Since,  however,  the  con- 
stant Kd  does  not  increase,  either  the  numerator  of  the  (fraction 


must  decrease  in  value,  the  denominator  increase,  or  both  changes 
must  take  place  simultaneously.  The  latter  happens.  A  part  of 
the  ammonia  combines  with  an  equivalent  quantity  of  hydrochloric 
acid  to  form  undissociated  ammonium  chloride.  This  reaction  pro- 
gresses until  again  the  mass  action  equation  is  satisfied.  In  this 
case,  when  equilibrium  is  again  established,  the  values  of  p'NHS  and 
p'HC1  are,  of  course,  no  longer  equal. 

Since,  according  to  the  theory  established  by  van't  Hoff,  the 
behavior  of  solutes  in  dilute  solutions  is  analogous  to  that  of  gases 
under  small  pressures,  it  may  naturally  be  assumed  that  relations 
entirely  similar  to  those  applying  in  the  case  of  the  dissociation  of 
ammonium  chloride  also  hold  for  electrolytes  which  dissociate  into 
two  ions.  For  example,  acetic  acid  in  dilute  aqueous  solutions  dis- 
sociates according  to  the  equation, 

CH3COOH  ^±  CH3COO'  +  H* 

Hence,  according  to  the  mass-action  law,  it  would  be  expected  that, 
at  constant  temperature,  the  following  equation  would  hold  :  — 

CH  X  CAe  C2 


CONDUCTANCE  OF  ELECTROLYTES  97 

In  this  equation  CH,  CAo,  and  CHAc  represent  the  active  or 
molar  masses  of  hydrogen  ions,  acetate  ions,  and  undissociated 
acetic  acid,  respectively,  and  Kd  a  constant,  called  the  dissociation 
constant,  which  is  characteristic  of  the  equilibrium  between  these 
three  substances  and  independent  of  the  individual  concentration  of 
each  substance  and  of  other  substances  which  may  also  be  present 
in  the  solution.  The  dissociation  constant  is  characteristic  of  the 
compound  and  its  determination  is  therefore  of  great  importance. 

In  order  to  show  the  existence  of  this  relation  between  the  disso- 
ciated and  undissociated  parts  of  an  electrolyte  in  dilute  solution,  it 
is,  of  course,  necessary  to  have  a  method  of  finding,  accurately,  the 
concentrations  of  the  ions  and  of  the  undissociated  molecules.  For 
this  purpose  the  determination  of  the  electrical  conductance  is  most 
satisfactory,  and  it  is  in  consequence  of  this  fact  that  conductivity 
measurements  are  of  such  great  value. 

This  method  of  testing  the  applicability  of  the  law  of  mass  action 
to  electrolytes  in  dilute  aqueous  solution  will  now  be  considered. 
A  mol  of  a  binary  electrolyte  is  dissolved  in  D  cubic  centimeters  of 
water,  in  which  it  dissociates  according  to  the  equation, 

A    ^±  A'  +  B'. 
The  mass-action  equation  for  this  case  is,  then,  — 


If  x=  the  degree  of  dissociation  of  the  electrolyte  or  that  frac- 
tion of  the  mol  which  is  broken  up  into  the  ions  A' 
and  B', 

and  1—  a;  =  the  fraction  of  the  mol  remaining  in  the  undissociated 
state  AB, 

then  —  =  concentration,   or  active  mass,  of   each  of  the  ions  A' 

and  B', 
and   ~~x  =  concentration,  or  active  mass,  of  the  undissociated  part, 

AB. 

By  substitution  of  these  values  in  the  above  mass-action  equation, 
the  following  is  obtained  :  — 

—  x    — 


1-a; 
D 


98  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

or  x2 


Kd 


It  is  evident  that,  in  order  to  determine  the  dissociation  constant, 
it  is  only  necessary,  to  know  the  dilution  D  and  the  degree  of  disso- 
ciation x  of  the  solute.  The  former  being  already  known,  the  latter 
is  determined  from  measurements  of  the  equivalent  conductance  of 
the  solution  at  the  two  dilutions,  D  and  infinity.  As  has  already 
been  stated,  the  dissociation  is  equal  to  the  ratio  of  the  former  to  the 
latter  conductance,  or,  otherwise  expressed, 


This  value  of  x  may  be  substituted  in  the  equation, 

*"         -K 

-* 


with  the  following  results :  — 

/TT      \2 

(if) 


01 


Before  proceeding  further  to  the  proof  of  this  formula,  it  is  advis- 
able to  become  acquainted  with  the  methods  used  for  the  determina- 
tion of  the  conductance  of  solutions. 

Determination  of  the  Electrical  Conductance  of  Electrolytes.  The 
Method  of  Kohlrausch.  —  By  an  application  of  Ohm's  law, 

F 

=  ~R~' 

the  resistance  of  metallic  conductors,  or  conductors  of  the  first  class, 
may  be  measured  in  a  very  simple  manner ;  but  this  is  not  the  case 
with  solutions  of  electrolytes,  or  conductors  of  the  second  class.  The 
gradual  fall  of  potential  F  which  exists  in  that  portion  of  the  circuit 
occupied  by  a  solution  is,  in  most  cases,  scarcely  to  be  determined 
accurately,  because  potential-differences  which  exist  at  the  electrodes 
and  the  solution  are  made  variable  by  the  nature  of  the  chemical 
decomposition  or  "  polarization  "  taking  place  there.  Many  methods, 
of  more  or  less  value,  have  been  devised  for  overcoming  this  diffi- 


CONDUCTANCE  OF  ELECTROLYTES  99 

culty.1  Of  these  methods  only  that  one  will  be  described  in  detail 
which  is  used  almost  exclusively  at  the  present  time  for  the  deter- 
mination of  the  electrical  conductance  of  electrolytes,  namely,  the 
Kohlrausch  method. 

This  method  depends  upon  the  use  of  an  alternating  current  of 
high  frequency,  and  of  non-corrodible  electrodes,  which  are  platin- 
ized in  order  to  increase  their  surfaces.  By  this  method  thex  dis- 
turbing influence  of  the  chemical  changes  at  the  electrodes,  or  the 
"  polarization,"  is  practically  removed ;  for  the  polarization  effect 
produced  by  the  current  when  flowing  in  one  direction  for  a  very 
small  fraction  of  a  second  is  practically  neutralized  by  the  effect 
produced  when  the  current  is  reversed  for  the  same  small  interval  of 
time.  The  disturbing  influence  being  thus  removed,  the  resistance 
of  the  solution  may  be  determined  exactly  as  in  the  case  of  the 
conductors  of  the  first  class. 

[The  apparatus  employed  is  essentially  a  Wheatstone  bridge. 
Therefore,  the  principle  of  a  Wheatstone  bridge  will  be  discussed 
before  considering  the  form  actually  used  in  the  determination  of  the 
conductance  of  solutions.  A  simple  form  of  such  a  bridge  is  shown 
in  Figure  28,  in  which  the  different  parts  are  named.  The  direct 


current  from  the  galvanic  cell  actuates  the  induction  coil,  thus 
causing  an  alternating  current  of  high  frequency  to  flow  through  the 
divided  circuit  consisting  of  the  two  branches  AC  and  ac,  respec- 
tively, which  are  uniform  wires  of  different  resistances  extending 
between  the  metal  bars  Aa  and  Cc. 

Let  us  now  consider  the  relation  between  the  fall  in  potential, 
the  resistance,  and  the  flow  of  the  electric  current  in  the  different 
parts  of  the  circuit  during  the  momentary  passage  of  electricity 
from  Aa  to  Cc,  assuming  the  potential  at  Aa  to  be  ten  units  and  at 
Cc  zero.  Then  along  each  of  the  two  wires  AC  and  ac  there  is  a 

1  Oitwald,  Lehrbuch  der  Allg.  Chemie,  Vol.  II,  1,  622. 


100  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

fall  of  potential  of  ten  units.  This  would  also  be  true  of  any  other 
wire,  whatever  its  resistance,  extending  between  the  bars  Aa  and 
Cc.  Since  the  two  wires,  although  of  widely  different  resistances, 
are  each  of  uniform  cross  section,  the  fall  of  potential  along  them 
will  be  uniform.  Thus  along  each  tenth  part  of  the  distance 
between  Aa  and  Cc  on  each  wire  there  will  be  a  fall  in  potential  of 
one  unit,  as  shown  by  the  numerical  values  in  the  figure.  These 
values,  then,  represent  the  potentials  of  the  different  points  along 
the  wires. 

If  now  the  point  B,  on  the  wire  AC,  at  which  the  potential  is 
seven  units,  be  connected  with  the  point  6,  on  the  wire  ac,  at  which 
the  potential  is  also  seven  units,  it  is  clear  that  no  electric  current 
will  flow  through  the  connecting  wire  Bb,  since  there  is  no  potential- 
difference  between  the  ends  of  the  wire.  If,  however,  the  point  B 
is  connected  with  the  point  &',  at  which  the  potential  is  nine  units, 
instead  of  with  6,  a  current  will  flow  through  the  wire  from  b'  to 
B,  since  a  potential-difference  exists  between  the  ends  of  the  wire. 
Finally,  if  the  point  B  is  connected  with  the  point  &",  at  which  the 
potential  is  five  units,  instead  of  with  &',  there  will  again  be  a 
difference  of  potential  of  two  units  between  the  ends  of  the  connect- 
ing wire,  and,  therefore,  an  electric  current  will  flow  through  it.  In 
this  case  the  direction  of  the  current  is  the  reverse  of  that  in  the 
previous  case.  It  may  then  be  stated  that  whenever  a  connecting 
wire  extends  between  equipotential  points  of  the  branches  of  a 
divided  circuit  no  current  flows  through  it.  In  all  other  cases 
a  current  does  flow  through  the  wire.  As  a  means  of  detecting 
whether  or  not  an  alternating  current  is  flowing  in  the  connecting 
wire  a  telephone  receiver  is  introduced  into  its  circuit  as  shown  in 
the  figure.  When  a  current  flows  (as  for  instance  when  B  and  6f 
are  connected)  a  humming  sound  is  heard  in  the  telephone.  If  now 
the  end  of  the  wire  at  6'  is  moved  along  the  wire  to  b  and  then  to 
6",  the  humming  sound  diminishes,  going  through  a  sharp  minimum 
when  the  point  6  is  reached,  and  rising  again  as  the  point  b"  is 
approached.  By  listening  at  the  telephone  it  is  then  possible  to 
tell  when  the  wire  connects  equipotential  points. 

It  is  at  once  evident  from  the  figure  that  when  the  wire  connects 
equipotential  points,  as,  for  example,  B  and  6,  the  following  relation 
exists  between  the  fall  in  potential  in  the  different  parts  of  the  two 
branches  of  the  divided  circuit,  otherwise  known  as  the  arms  of  the 
Wheatstone  bridge :  — 

Fall  in  AB :  Fall  in  BC  =  Fall  in  ab  :  Fall  in  be. 


CONDUCTANCE   OF  ELECTROLYTES 


101 


Recalling  to  mind  the  fact  that  the  falls  in  potential  in  the  differ- 
ent parts  of  a  circuit  are  directly  proportional  to  the  respective 
resistances  of  the  parts,  in  this  case  it  follows  that 

Resistance  AB :  Resistance  BC  —  Resistance  ab  :  Resistance  be. 

If  now  the,  ratio  of  any  two  of  these'  resistances,  such  as,  for 
example,  the  ratio  of  the  resistance  of  ab  to  that  of  6c,  and  the 
actual  value  of  either  of  the  two  resistances,  AB  or  BCy  are  known, 
then  the  fourth,  or  the  unknown  resistance,  may  be  calculated  from 
the  above  proportion. 

In  this  manner  unknown  resistances  may  be  determined  by  means 
of  the  Wheatstone  bridge. 

When  the  resistance  of  an  electrolyte  is  to  be  determined 
the  Wheatstone  bridge  is  arranged  as  shown  in  Figure  29.1  The 


10      20     30      40     50     60     70     60     00 
FIG.  29 

similarity  between  this  figure  and  the  one  directly  preceding  it  is 
at  once  evident.  In  this  figure  the  two  branches  of  the  divided 
circuit  are  abc  and  aABc,  respectively.  The  former  branch  includes  a 
resistance  box,  by  means  of  which  various  known  resistances  can  be 
introduced  into  the  circuit,  and  the  conductivity  cell  containing  the 
solution  to  be  investigated.  The  resistances  in  the  resistance  box 
and  in  the  conductivity  cell  are  so  great  that  those  of  the  connecting 
wires  in  this  branch  may  be  neglected.  The  branch  abc  consists  of  a 
platinum  wire  of  uniform  resistance,  which  is  either  stretched  over  a 
meter  scale  or  wound  on  a  drum,  which  is  marked  off  in  millimeter 
lengths.  One  end  of  the  connecting  wire  Cb  is  made  fast  at  any 
point  C  between  the  resistance  box  and  the  conductivity  cell,  while 
the  other  end  b  is  connected  with  the  platinum  wire  by  means  of  a 
sliding  contact.  The  position  of  this  sliding  contact  may  be  read 
off  on  the  meter  or  drum  scale  to  tenths  of  a  millimeter.  In  series 

1  Ostwald,  Ztschr.  phys.  Chem.,  2,  561  (1888). 


102 


A   TEXT-BOOK  OF*  ELECTRO-CHEMISTRY 


with  the  connecting  wire  is  a  telephone  receiver  (naturally  a  galva- 
nometer cannot  be  used),  which  serves  to  determine  when  the 
sliding  contact  is  in  such  a  position  that  no  current  flows  through 
the  wire,  i.e.  when  the  wire  connects  equipotential  points.  The 
four  arms  of  the  Wheatstone  bridge  are  then  ab,  be,  aAC,  and  CBc. 
Hence  when  the  sliding  contact  is  in  the  position  giving  a  minimum 
tone  in  the  telephone  receiver,  the  following  relations  obtain :  — 

Resistance  of  ab  _  Resistance  in  box 
Resistance  of  be      Resistance  in  cell 

If  the  platinum  wire  is  of  uniform  resistance,  we  have  — 

Resistance  of  ab  _  Distance  ab 

Resistance  of  be      Distance  be 
Therefore, 

Resistance  in  cell  =  Resistance  in  box  x 


Distance  be 
Distance  ab' 


or, 


=  B    X 


bc_ 
ab 


The  absolute  value  of  the  resistance  of  the  platinum  wire  evidently 
does  not  come  into  consideration,  since  only 
the  ratio  of  the  resistances  of  the  two  parts 
of  it  is  required.] 

A  vessel,  such  as  is  shown  in  Figure  30,1 
can  in  most  cases  be  used  for  the  determina- 
tion of  the  conductance  of  an  electrolyte. 

The  area  of  the  electrodes  and  the  distance 
between  them  can  be  varied  as  desired.  In 
general,  it  is  advantageous  to  platinize  them, 
using  a  solution  containing  about  three  per 
cent  of  commercial  platinic  chloride  and 
about  0.025  per  cent  of  lead  acetate. 

If  the  distance  in  centimeters  between  the 
two  electrodes  is  represented  by  I,  and  their 
area  in  square  centimeters  by  s,  then  the 
value  of  the  specific  conductance  K  is  given  by  the  following 
equations:  — 

1          ab  s 


FIG.  30 


K  =  —  = 


»    ~ir  ^ 

K3  x  be         I 


Hence 


1  For  other  forms  of  conductivity  cells,  see  Ostwald-Luther's  Physik.-chem 
Messungen,  page  401. 


CONDUCTANCE  OF  ELECTROLYTES        103 

From  the  specific  conductance  K,  and  the  equivalent  dilution  of 
the  solution  D  in  cubic  centimeters,  the  value  of  the  equivalent 
conductance  can  be  calculated  in  the  manner  described  on  page  86, 
with  the  aid  of  the  equation, 

K  =  K  X  D, 

providing  the  cross  section  of  the  vessel  and  the  areas  of  the  elec- 
trodes are  practically  the  same.  In  order  to  avoid  this  proviso  and 
to  obviate  the  necessity  of  measuring  the  space  between  the  elec- 
trodes, it  is  usual  to  determine  the  so-called  "  cell  constant "  of  the 
conductance  cell.  The  cell  constant  is  equal  to  the  resistance  found 
in  the  cell  when  it  contains  between  the  electrodes  a  solution  of  a 
specific  conductance,  or  conductivity,  of  unity.  In  this  cell,  since 
the  conductivity  of  the  solution  is  unity, 

RZ  =  I  x  k  =KC, 

s 

where  R^  is  the  measured  resistance,  k  a  constant  depending  upon 
the  form  of  the  cell  and  the  position  of  the  electrodes  in  reference 
to  the  cell  walls,  and  Kc  the  cell  constant.  When  the  surfaces  of 
the  electrodes  are  equal  to  the  cross  section  of  the  cell,  the  value  of  k 
becomes  unity. 

It  is  not  at  all  necessary,  however,  to  have  a  solution  whose 
specific  conductance  is  unity  in  order  to  obtain  the  value  of  the  cell 
constant.  It  can  be  obtained  with  the  aid  of  any  liquid  of  known 
conductance.  Thus,  if  the  specific  conductance  of  the  liquid  is  s, 
and  its  resistance  when  in  the  cell  whose  constant  is  to  be  deter- 
mined is  R,  then  the  value  of  the  cell  constant  Kc  is  given  by  the 
equation, 

Kc  =   R  X  K. 

When  the  cell  constant  is  known,  the  specific  and  equivalent  con- 
ductances of  any  liquid  may  be  obtained  with  the  use  of  the 
equations, 


where  RX  is  the  resistance  of  the  liquid  as  measured  directly  on  the 
Wheatstone  bridge.  If  the  conductance  of  the  liquid  used  to 
obtain  the  cell  constant  is  expressed  in  ohms,  then  the  specific  or 
the  equivalent  conductance,  calculated  according  to  the  above  equa- 
tions, is  also  expressed  in  ohms,  even  though  the  resistance  in  the 
resistance  box  used  both  to  obtain  the  cell  constant  and  to  obtain  the 
unknown  conductance  is  expressed  in  other  units. 


104 


A   TEXT-BOOK   OF  ELECTRO-CHEMISTRY 


In  determining  the  cell  constant,  a  0.02  normal  solution  of  potas- 
sium chloride  is  often  used  as  the  liquid  of  known  conductance. 
According  to  the  most  recent  measurements,  its  specific  conductance, 
or  conductivity,  at  18°  and  at  25°  is 


K180  =  0.002399,  and 


0.002773, 


while  its  corresponding  equivalent  conductance  is 
g180  =  119.96,  and  K^O  =  138.67. 

The  value  of  the  equivalent  conductance  is  a  large  one.  The  re- 
sistance of  one  equivalent  of  potassium  chloride  in  this  solution, 
when  placed  between  electrodes  one  centimeter  apart,  is  accordingly 

jj^  and    j^  ohms,  respectively. 

The  equivalent  conductances  of  all  binary  electrolytes,  at  infinite 
dilution,  are  of  the  same  order  of  magnitude,  varying  between  50 
and  500,  as  may  be  seen  from  the  table  on  page  93.  On  the  other 
hand,  the  value  of  the  equivalent  conductance,  at  other  dilutions, 
may  be  exceedingly  small  for  some  electrolytes.  This  will  be  evi- 
dent from  a  glance  at  the  table  on  page  88. 

Method  of  Nernst  and  Haagn.1  —  This  method  of  determining  con- 
ductance permits  an  easy  measurement  of  the  internal  resistance  of 
a  cell  even  while  a  current  is  passing  through  it.  It  is  characterized 
by  the  use  of  two  condensers,  in  place  of  two  of  the  resistances 
employed  in  the  Wheatstone  bridge.  The  arrangement  of  the 
apparatus  is  shown  in  Figure  31. 


FIG.  31 

The  condenser  C3  is  used  to  prevent  closing  the  circuit  of  the  cell 
C,  the  internal  resistance  of  which  is  to  be  measured.     Under  these 

i  Ztschr.  Elektrochem.,  2,  493  (1896)  ;  Ztschr.phys.  Chem.,  23,  97  (1897). 


CONDUCTANCE   OF   ELECTROLYTES  105 

circumstances  the  cell  produces  no  current.  After  the  known  re- 
sistance R  has  been  varied  until  a  minimum  tone  is  heard  in  the 
telephone  receiver,  the  value  of  the  unknown  resistance  RZ  of  the  cell 
C  may  be  calculated  from  the  equation, 

Rz  :  R  =  C2  :  C1? 

where  C2  and  Cx  represent  the  respective  capacities  of  the  two  lower 
condensers.  The  ratio  02:0!  must  be  determined  independently. 
This  can  be  done  by  means  of  an  ordinary  Wheatstone  bridge. 

In  order  to  obtain  the  internal  resistance  of  a  cell  while  producing 
an  electric  current,  the  cell  is  short-circuited  through  a  known  re- 
sistance as  indicated  in  the  figure  by  the  dotted  line.  It  must  be 
clearly  understood  that  the  real  internal  resistance  RZ  of  the  cell  is 
not  obtained  by  direct  measurement,  but  is  obtained  from  the  meas- 
ured resistance  RZ'  and  from  the  resistance  of  the  dotted  shunt  cir- 
cuit, according  to  the  equation  :  — 

p  ==          r       ft  • 

Rx  |          Rz  Rj,. 

The  value  of  RX"  may  be  obtained  with  sufficient  exactness  from  the 
equation, 


Calculation  of  the  Dissociation  Constant  from  Electrical  Conduc- 
tance. —  It  has  already  been  shown  that  the  dissociation  constant 
may  be  calculated  by  the  aid  of  the  equation, 


In  order  to  obtain  the  value  of  the  constant,  it  is  therefore  neces- 
sary to  know  both  the  value  of  the  equivalent  conductance  at  dilu- 
tion D,  or  KB,  and  that  at  dilution  infinity,  or  K^.  The  method  of 
obtaining  the  value  of  KD  has  already  been  considered.  In  some 
cases  the  value  of  K^  may  be  obtained  by  the  same  method,  it  being 
placed  equal  to  the  maximum  value  of  the  equivalent  conductance 
found  upon  diluting  the  solution.  This  method  is  applicable  only 
to  electrolytes  which  dissociate  to  a  large  degree  in  solutions  of 
ordinary  dilutions.  It  is  not  applicable  to  other  electrolytes,  be- 
cause, at  the  extreme  dilutions  at  which  the  value  of  K  could  be  con- 
sidered equal  to  K^,  it  is  impossible  to  determine  the  conductance  of 
the  solution.  This  is  the  case  with  practically  all  organic  acids  and 
bases,  where  a  knowledge  of  the  value  of  the  dissociation  constant  is 


106  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

of  special  importance.  Fortunately,  however,  the  alkali  salts  of  all 
acids  and  the  halogen  salts  of  practically  all  bases  are  largely  dissoci- 
ated in  moderately  dilute  solutions,  and  nearly  completely  dissociated 
in  solutions  the  conductance  of  which  can  still  be  determined.  Thus 
the  value  of  K^  for  these  salt  solutions  may  be  determined  by  direct 
experiment.  But  this  value  has  been  shown  to  be  equal  to  the  sum 
of  the  migration  velocities  of  anion  and  cation  :  — 


[In  the  case  of  the  alkali  salt  of  a  slightly  dissociated  acid  HA,  K^ 
may  be  determined  directly,  and  uc  is  a  known  value.  The  value  of 
ua  for  the  anion  A'  is  thereby  determined.  But  the  value  of  uc  for 
the  cation  H',  is  a  known  value.  Hence  the  value  of  KX  for  the  acid 
HA  may  at  once  be  obtained  by  adding  together  the  known  migra- 
tion velocities  of  its  ions.  Thus 

K,  (for  HA)  =  uc  (for  H*)  +  ua  (for  A'). 

In  a  similar  manner  the  equivalent  conductance  at  infinite  dilution 
for  a  slightly  dissociated  base,  BOH,  may  be  obtained.  For  its 
halogen  salt,  K^  can  be  determined  directly,  and  ua  for  the  halogen 
ion  is  known.  Hence  the  value  of  uc  for  the  cation  B*  is  known. 
From  this  value  and  the  known  value  of  ua  for  the  anion  OH'  the 
equivalent  conductance  of  the  base  BOH  at  infinite  dilution  may 
be  obtained  by  the  aid  of  the  equation, 

K^  (for  BOH)  =  uc  (for  B')  +  ua  (for  OH'). 

In  the  above  explanation  of  the  indirect  method  of  determining 
the  value  of  the  equivalent  conductance  of  a  slightly  dissociated  acid 
or  base  at  infinite  dilution,  the  individual  migration  velocities  of  the 
ions  were  involved.  This  is  not  at  all  necessary  in  making  actual 
calculations,  as  will  be  made  evident  from  a  reconsideration  of  the 
above  acid  HA.  The  value  of  K^,  for  example,  of  hydrochloric  acid, 
of  sodium  chloride,  and  of  the  sodium  salt  of  the  acid  HA  may  be 
obtained  from  direct  measurements  on  very  dilute  solutions.  Hence 
the  three  equations, 

K^  (for  HC1)  =uc  (for  H*)  +ua  (for  Cl'); 
K^  (for  NaCl)  =  uc  (for  Na  )  +  ua  (for  Cl'); 
K^  (for  NaA)  =  uc  (for  Na)  +  u0  (for  A'). 

Combining  these  equations, 

K,  (HC1)  -  5,  (NaCl)  +  5,  (NaA)  =  ue  (IT)  +  w.  (A1)  ; 
S.  (HC1)-B.  (NaCl)  +  S,  (NaA)  =  Sa>  (HA). 


CONDUCTANCE  OF   ELECTROLYTES 


107 


The  latter  equation,  in  which  migration  velocities  do  not  appear,  may 
be  used  for  the  calculation  of  the  value  of  K^  for  the  acid  in  ques- 
tion.] As  is  evident,  it  is  only  necessary  to  add  to  the  difference  of 
the  values  of  K^  for  hydrochloric  acid  and  sodium  chloride,  the  value 
of  K^  for  the  sodium  salts  of  any  slightly  dissociated  acid,  to  obtain 
the  equivalent  conductance  of  the  latter  acid  at  infinite  dilution. 
The  values  of  K^  for  hydrochloric  acid  and  sodium  chloride  accord- 
ing to  most  recent  measurements,  and  their  differences,  are  given  in 
the  following  table  :  — 


TEMPERATURE 

KOO  FOR  HC1 

2Lo  FOR  NaCl 

DIFFERENCE 

18° 

383.4 

108.9 

274.5 

25° 

427.1 

126.6 

300.5 

From  the  values  of  the  equivalent  conductance  at  the  dilution  D 
and  at  the  dilution  infinity,  obtained  as  above  described,  the  dissoci- 
ation constants  have  been  calculated  for  a  large  number  of  slightly 
dissociated  acids  and  bases  at  different  dilutions.  It  was  found  that 
the  constants  are  independent  of  the  concentration.  The  results 
obtained  for  acetic  acid  are  given  in  the  following  table :  — 


EQUIVALENT  CONCENTRATION 


DISSOCIATION  CONSTANT  x  105. 


0.00180 
0.00179 
0.00182 
0.00179 
0.90179 
0.00180 
0.00180 
0.00177 


The  value  of  the  dissociation  constant  may  serve  in  many  cases 
as  a  trustworthy  aid  in  the  identification  of  a  compound.1 

Since  a  consideration  of  the  significance  of  this  constant  belongs 
to  the  subject  of  chemical  statics,  it  will  not  be  discussed  further 
here.  It  may  be  well  to  state,  however,  that  the  order  of  magni- 
tudes of  these  constants  for  different  compounds  is  also  the  order  of 
their  degrees  of  dissociation  in  solutions  of  the  same  equivalent 
concentration.  A  direct  proportionality  does  not  exist  between  the 
constants  and  the  degrees  of  dissociation,  for,  as  the  dilution  is  in- 
creased, the  latter  approaches  a  constant  value.  Nevertheless,  some 


^cudder,  J.  Phy.  Chem.,  7,  269  (1903). 


108  A   TEXT-BOOK   OF  ELECTRO-CHEMISTRY 

conclusions  from  the  existence  of  such  constants,  which  were  em- 
pirically  established  by  Ostwald  before  the  dissociation  theory  was 
proposed,  will  be  considered. 

1.    With  increasing  value  of  D  in  the  equation, 


the  left-hand   side  finally  becomes  infinite.      Since  KD  and  K^  are 
always  finite  quantities,  this  can  only  be  true  when 


The  equivalent  conductance  approaches  its  value  at  infinite  dilution 
as  the  dilution  is  increased. 

2.  In  the  case  of   slightly  dissociated,  and  consequently  poorly 
conducting,  binary  electrolytes,  where  KD  is  very  small  in  compari- 
son with  K^,  the  expression  (K^  —  K^)  changes  but  slightly  with  the 
dilution  and  may  therefore  be  considered  as  a  constant.     Hence  the 
equation, 

^  =  Constant. 

The  equivalent  conductance  increases  with  increasing  dilution  in  pro- 
portion to  the  square  root  of  the  dilution;  or  the  square  of  the  equiva- 
lent conductance  increases  in  proportion  to  the  dilution. 

3.  If  the  mass-action  equation  for  the  dissociation  be  written  in 
its  original  form  as  follows  :  — 


- 


then  for  substances  which  dissociate  but  slightly,  the  value  of  1  —  x 
may  be  considered  as  unity  without  serious  error  and  the  equation 
assumes  the  form, 


In  the  case  of  slightly  dissociated  electrolytes,  the  dissociation  constant 
varies  directly  as  the  square  of  the  percentage  dissociation  and  inversely 
as  the  dilution. 

4.  According  to  the  derivation  given  in  No.  2,  the  following  equa. 
tionshold  for  two  or  more  slightly  dissociated  electrolytes  :  — 


-^-  =  Constant, 
and  n    =  Constant,  etc. 


CONDUCTANCE  OF   ELECTROLYTES  109 

These  two  equations  may  be  combined,  resulting  in  the  equation, 


=  Constant. 

) 

D" 

If  now  the  dilution  of  one  of  the  electrolytes  (Z)')  is  equal  to  that 
of  the  other  (I)"),  then  the  equation  becomes 

£^  =  Constant.  (a) 

\£  D) 

From  the  equations  derived  in  No.  3,  it  may  be  shown  in  a  similar 
manner  that  the  following  equation  holds  :  — 


In  the  above  equations,  K'^,  a;',  K'd,  and  £%  x",  and  K"d  represent 
the  equivalent  conductances  at  dilution  D,  the  degrees  of  dissocia- 
tion, and  the  dissociation  constants  of  the  two  electrolytes  respec- 
tively. It  has  been  shown  that 


Hence  for  the  above  electrolytes  we  have  the  equation, 


If  now  the  value  of  K'^  is  equal  to  that  of  B/^,  such  as  is  the 
case  with  many  acids  because  of  the  very  great  migration  velocity  of 
the  ion  which  they  have  in  common  (the  hydrogen  ion),  this  equa- 
tion becomes 

1^  =  ^-.  (c) 

K"        r"  V' 

K  D      X 

Combining  equations  (6)  and  (c),  the  following  equation  results  :  — 

=  K'd 


The  squares  of  the  equivalent  conductances  of  different  electrolytes  at 
the  same  dilution  are  to  each  other  as  the  corresponding  dissociation 
constants. 

5.   In  the  equation  — 


- 


110  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

the  value  of  K^  may,  in  the  case  of  electrolytes  which  dissociate  to 
a  large  degree,  be  considered  as  remaining  practically  constant  with 
increasing  dilution,  and  as  K^  is  in  itself  constant,  the  equation 
becomes 

=  Constant. 


The  difference  between  the  equivalent  conductance  at  a  given  dilution 
and  that  at  the  dilution  infinity  multiplied  by  the  former  dilution  gives  a 
constant  value. 

6.  In  the  case  of  electrolytes  which  dissociate  to  a  large  extent, 
the  value  of  the  percentage  dissociation  x  may  be  considered  as 
approximately  equal  to  unity.  The  equation 


may  then  be  written  in  the  simple  form, 

*-  or  i- 


The  undissociated  portion  of  an  electrolyte  multiplied  by  the  dilution 
is  equal  to  the  reciprocal  of  the  dissociation  constant. 

According  to  this  statement,  it  is  evident  that  if  the  undissociated 
portion  at  an  equivalent  dilution  of  50,000  cubic  centimeters  amounts 
to  one  per  cent,  it  will  amount  to  only  one  half  per  cent  at  a  dilu- 
tion of  100,000  cubic  centimeters. 

7.  According  to  the  derivation  of  No.  5,  the  following  equations 
hold  for  any  two  electrolytes  which  are  largely  dissociated  :  — 

(K'OO  -K  '&)&'  =  Constant, 
and  (K"W  -K  V)#"  =  Constant. 

These  equations  combined  give  the  following  :  — 


When  the  dilution  of   one  electrolyte  D?  is  equal  to  that  of  the 
other  D",  this  equation  becomes  — 


=  Constant.  (a) 


In  a  similar  manner,  from  the  derivation  of  No.  6  the  following 
equation  may  be  obtained  :  — 


CONDUCTANCE   OF  ELECTROLYTES  111 


The  latter  equation  may  be  expressed  in  words  as  follows  :  — 

The  undissociated  portions  of  different  electrolytes  at  the  same  equiva- 

lent dilution  are  inversely  proportional  to  their  dissociation  constants. 
When  the   equivalent  conductances   of   the   two   electrolytes  at 

infinite  dilution  are  nearly  the  same,  equations  (a)  and  (6)  may  be 

combined,  giving  the  approximate  equation, 

SL-S'*  =K"d 
*"«-&"*     JT/ 

The  differences  between  the  equivalent  conductance  at  a  given  dilution 
and  that  at  infinite  dilution  of  two  electrolytes  are  inversely  propor- 
tional to  their  dissociation  constants. 

8.  Finally,  the  following  regularities  for  all  electrolytes  may  be 
deduced.  If  two  electrolytes  are  dissociated  to  the  same  extent, 
then  the  left  side  of  the  equation, 


is  the  same  for  both,  and,  consequently,  the  same  is  true  of  the 
right  side. 

Hence  the  equation, 


or  D»      JCd 

The  equivalent  dilutions  at  which  different  electrolytes  possess  the 
same  degree  of  dissociation  (and  also  often  nearly  the  same  equivalent 
conductance)  are  in  a  constant  ratio  to  each  other,  which  is  equal  to 
the  inverse  ratio  of  the  respective  dissociation  constants. 

The  foregoing  approximations  may  often  be  used  with  advantage. 

Relation  between  Dissociation  Constants  and  Chemical  Constitu- 
tion. Some  very  interesting  relations  have  been  found  between  the 
magnitudes  of  the  dissociation  constants  and  the  chemical  constitu- 
tion of  acids,  as  may  be  illustrated  by  a  few  examples.  The  con- 
stants (Kd-  105)  for  acetic  acid  and  the  three  chloracetic  acids,  at  25°. 
are  as  follows  :  — 

Acetic  acid     .....  (CH3COOH)  ....      0.00180 

Monochloracetic  acid  .     .  (CH2C1COOH)  ....       0.155 

Dichloracetic  acid  .     .     .  (CHC12COOH)  ....       5.14 

Trichloracetic  acid       .     .  (CC13COOH)  ....  121. 


112  A   TEXT-BOOK  OF   ELECTRO-CHEMISTRY 

Thus  the  replacement  of  the  hydrogen  by  chlorine  causes  a  very 
large  increase  in  the  value  of  the  constant.  That  this  increase  is 
not  the  same  for  the  successive  replacements  by  chlorine  is  evident 
from  the  following  table :  — 


REPLACEMENT 

INCREASE  IN  CONSTANT 

First 
Second 
Third 

°-155      or  86  fold 

0.00180' 
|§,or33.2fo.d. 

—  ,  or  23.  5  fold. 
5.14 

It  may  be  concluded  from  this  that  the  introduction  of  chlorine 
into  acetic  acid  produces  an  effect  somewhat  different  from  that 
which  it  produces  when  introduced  into  chloracetic  acid.  This  is 
not  surprising,  since  a  chlorine  atom  is  already  present  in  the  latter 
compound.  An  increase  in  the  value  of  the  dissociation  constant 
indicates  an  increase  in  the  degree  of  dissociation,  and  also  an 
increase  in  the  intensity  of  its  acid  character.  The  replacement 
of  hydrogen  by  chlorine  produces  an  effect  in  this  direction.  The 
introduction  of  such  other  so-called  negative  radicals  as  Br,  ON, 
SON,  OH,  etc.,  also  increases  the  acid  character  of  the  original  com- 
pound in  a  similar  manner. 

The  a  and  /?  substituted  derivatives  of  acids  possess  very  different 
dissociation  constants,  thus  showing  the  marked  constitution  prop- 
erty of  this  constant.  The  same  applies  to  the  isomeric  derivatives 
of  benzene,  for  example  :  — 

Benzoicacid C6H5COOH  .   ,..,./-.,.  .  .  0.006 

o-Hydroxybenzoic  acid      .     .  o-C6H4(OH)COOH     .  .  .  0.102 

m-Hydroxybenzoic  acid     .     .  m-C6H4(OH)COOH    .  .  .  0.0087 

p-Hydroxybenzoic  acid      .     .  p-C6H4(OH)COOH     .  .  .  0.00286 

These  examples  show  that  a  knowledge  of  the  dissociation  con- 
stant is  of  aid  in  the  determination  of  the  chemical  constitution  of 
compounds.  By  the  introduction  of  an  hydroxyl  group  into  benzoic 
acid  in  the  ortho  position,  the  constant  for  the  acid  is  increased 
seventeen  fold.  When  the  same  group  is,  instead,  substituted  in 
the  meta  position,  the  change  from  the  benzoic  acid  value  is  slight, 
but  still  positive,  while  an  entrance  into  the  para  position  even 
causes  a  considerable  reduction  of  the  constant.  Consequently,  it 
might  be  assumed  that  if  a  series  of  acids  be  formed  by  introducing 


CONDUCTANCE  OF   ELECTROLYTES  113 

hydroxyl  groups  into  ortho-oxybenzoic  acid,  their  dissociation  con- 
stants would  vary  in  a  similar  manner.  That  this  is  the  case  is 
evident  from  a  consideration  of  the  following  table  :  —7 

o-Oxybenzoic  (salicylic)  acid  C6H4(OH)COOH       .....  0.102 

Hydroxysalicylic  acid  .     .     C6H3(OH)2COOH  (2,  3)      ...  0.114 

Hydroxysalicylic  acid  .     .     C6H3(OH)2COOH  (2,  5)     ...  0.108 

Kesorcylic  acid     ....     C6H3(OH)2COOH  (2,  4)      ...  0.052 

Kesorcylic  acid     ....     C6H3(OH)2COOH  (2,  6)      ...  5.0 

In  the  acid  (2,  3)  and  also  in  the  acid  (2,  5)  the  new  hydroxyl 
group  is  in  the  meta  position  in  relation  to  the  carboxyl  group. 
Consequently,  only  a  very  slight  increase  in  the  dissociation  constant 
is  to  be  expected.  This  agrees  with  experimental  observation. 

In  the  acid  (2,  4)  the  new  hydroxyl  group  occupies  the  para  posi- 
tion, and,  as  in  the  case  of  hydroxybenzoic  acids,  a  new  constant,  less 
than  the  original  one,  results.  Finally,  when  the  second  hydroxyl 
group  occupies  the  remaining  ortho  position,  as  in  the  acid  (2,  6),  a 
corresponding  great  increase  in  the  constant  is  found,  the  increase 
being  about  fifty  fold. 

Interesting  relations  have  been  found  in  the  case  of  the  dissocia- 
tion in  stages  of  dibasic  organic  acids.  From  the  fact  that  the  mass- 
action  equation  for  the  dissociation  of  binary  electrolytes  holds  also 
for  weak  dibasic  acids,  it  follow  that  the  dissociation  takes  place  at 
first  according  to  the  equation, 


(a) 

Only  in  the  case  of  strong  acids  does  a  further  dissociation  according 
to  the  equation 

HE/^H'+R"  (6) 

take  place.     In  such  cases  the  equation 


derived  for  binary  electrolytes,  naturally  does  not  apply.  Dif- 
ferent dibasic  or  polybasic  acids  are  strikingly  characterized  by  the 
way  in  which  they  dissociate.  While  in  the  case  of  some  acids 
the  dissociation  of  the  second  hydrogen,  'according  to  equation  (6), 
takes  place  only  after  that  of  the  first  hydrogen,  according  to  equa- 
tion (a),  is  nearly  complete,  in  the  case  of  other  acids  the  dissociation 


114  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

of  the  second  hydrogen  takes  place  to  some  extent  when  but  fifty  per 
cent  of  the  first  hydrogen  is  dissociated.  This  difference  is  evident 
in  the  titration  of  acids  with  indicators.  Sulfurous  acid,  for  example, 
when  titrated,  using  litmus  as  an  indicator,  gives  no  sharp  end  point, 
the  dissociation  of  the  second  hydrogen  being  too  slight.  However, 
succinic  acid,  which  in  respect  to  the  first  hydrogen  ion  is  far  less 
dissociated  than  sulfurous  acid,  may  be  easily  titrated  with  the  use 
of  this  indicator. 

Between  the  dissociation  constant  for  the  dissociation  of  the  first 
hydrogen  atom  (dissociation  constant  of  the  free  acid)  and  the  corre- 
sponding constant  for  that  of  the  second  hydrogen  atom  there  exists 
the  following  relation  :  — 

1.  The  first  hydrogen  atom  is  dissociated  to  the  greater,  and  the  sec- 
ond  to  the  lesser  extent,  the  nearer  the  two  carboxyl  groups  are  to  each 
other.  The  reverse  is  also  true. 

This  statement  was  first  made  by  Smith,1  who  based  it  upon  his 
own  work  and  also  that  of  Ostwald  and  Noyes. 

As  an  illustration  of  this  principle,  the  following  quotation  from 
Ostwald  is  given,  in  which  it  is  assumed  that  the  electrical  charge  of 
the  acid  ion  is  localized  on  the  hydroxyl  oxygen  of  the  carboxyl 
group  :  — 

"In  the  case  of  the  dissociation  of  the  first  hydrogen  atom  of 
dibasic  organic  acids,  the  one  carboxyl  group  exerts  a  negative  influ- 
ence upon,  and  tends  to  increase  the  degree  of  the  dissociation  of,  the 
other  carboxyl  group.  This  tendency  is  the  stronger,  the  nearer  the 
two  carboxyl  groups  are  to  each  other.  If  the  first  stage  of  the  dis- 
sociation takes  place  according  to  the  equation 


then  the  second  stage,        HE'  H*^:  +  E" 

will  in  general  take  place  far  more  difficultly  than  the  first  stage, 
since  the  negatively  charged  ion  HE,'  in  dissociating  must  take  up 
an  extra  negative  charge  to  form  the  ion  E",  and  since  the  two 
negative  charges  repel  one  another.  Secondly,  the  ease  with  which 
the  second  stage  of  the  dissociation  will  take  place  depends  upon 
the  distance  between  the  charges.  Thus  the  nearer  the  charges  on 
a  bivalent  ion  are  to  each  other,  the  less  is  the  tendency  of  the 
hydrogen  atom  to  split  off,  and  conversely." 

The  behavior  of  fumaric  and  maleic  acids  is  in  complete  agree- 

1  Ztschr.  phys.  Chem.,  25,  144  (1898). 


CONDUCTANCE  OF  ELECTROLYTES 


115 


ment  with  the  above  principle  and  hypothesis.     This  will  be  evi- 
dent from  a  study  of  the  following  formulae  and  tables :  — 


H-C-COOH 
Maleic  Acid  II 

H-C-COOH 


H-C-COOH 


Fumaric  Acid 


HOOC-C-H 


MOL.  DILUTION 

%  DISSOCIATION 

Kd  x  10« 

%  DISSOCIATION 

KdxlO« 

128 

68.8 

1.16 

29.3 

0.095 

256 

78.8 

1.14 

39.0 

0.097 

512 

87.1 

1.15 

50.3 

0.099 

1024 

92.8 

1.17 

63.9 

0.110 

2048 

98.2 

— 

78.5 

0.140 

The  per  cent  dissociation  is  calculated  on  the  assumption  that  the 
acids  dissociate  as  if  they  were  monobasic. 

The  carboxyl  groups  in  the  fumaric  acid  molecule  are  farther 
apart  than  those  in  the  maleic  acid  molecule.  Corresponding  to 
this,  the  dissociation  constant  is  much  less  in  the  former  than  in  the 
latter  case.  On  the  other  hand,  the  dissociation  of  the  second  hy- 
drogen takes  place  appreciably  in  the  case  of  maleic  acid  only  after 
a  nearly  complete  dissociation  of  the  first  hydrogen  atom,  while  in 
the  case  of  fumaric  acid  it  takes  place  when  but  about  fifty  per  cent 
of  the  first  hydrogen  atom  is  ionized.  This  is  indicated  in  the  above 
tables  by  the  increase  in  the  value  of  the  constant.  The  acid  salts 
show  an  analogous  behavior  in  respect  to  the  dissociation  of  the 
second  hydrogen  atom.  At  a  molar  dilution  of  64,  the  dissociation 
of  this  atom  is  0.39  per  cent  in  the  case  of  the  acid  salt  of  maleic, 
and  0.85  per  cent  in  that  of  fumaric,  acid. 

The  effect  of  substituted  groups  in  organic  dibasic  acids  upon  the 
dissociation  of  the  second  hydrogen  atom  is  expressed  in  the 
following  statement :  — 

2  a.  The  degree  of  dissociation  of  the  second  hydrogen  atom  of  all 
substituted  acids  is  less  than  that  of  the  original  acid,  except  in  the 
case  of  liydroxyl  substituted  acids,  in  which  it  is  increased. 

Thus  the  dissociation  of  the  second  hydrogen  atoms  of  methyl- 
and  ethyl-succiuic  acids  is  less,  and  of  the  hydroxysuccinic  acids, 
malic  and  tartaric  acids,  is  greater,  than  that  of  succinic  acid  itself. 

The  relation  between  the  dissociation  constants  of  the  first  and 
second  hydrogen  acids  of  analogous  substituted  dibasic  acids  may 
be  expressed  as  follows :  — 

2b.    The  dissociation  constant  (K"d)  of  the  second  hydrogen  atom 


116  A   TEXT-BOOK   OF  ELECTRO-CHEMISTRY 

of  a  substituted  add  is  the  smaller,  the  greater  the  constant  (K'd)  of 
the  first  hydrogen  atom.  In  other  words,  the  substituted  groups  affect 
the  dissociation  of  the  two  hydrogen  atoms  oppositely. 

While,  for  example,  the  value  of  K'd  for  methyl-  and  ethyl-succinic 
acids  is  greater,  the  value  of  K"d  for  these  acids  is  less  than  the 
corresponding  constant  Kd  for  succinic  acid. 

A  knowledge  of  the  dissociation  constant  of  the  second  hydrogen 
atom  would  undoubtedly,  in  many  cases,  be  of  an  importance  equal 
to  that  of  the  first  hydrogen,  in  the  study  of  the  constitution  of 
dissolved  substances.1 

Finally,  it  should  be  mentioned  that  with  the  aid  of  the  dissocia- 
tion constants  of  weak  acids  the  degree  of  hydrolysis  of  their  alkali 
salts  may  easily  be  calculated.2 

Velocity  of  Migration  of  Individual  Ions.  —  From  conductance 
measurements  not  only  have  the  dissociation  constants  of  a  large 
number  of  organic  acids  and  bases  been  determined,  but  also  the 
relative  velocities  of  migration  of  the  organic  cations  and  anions. 
It  has  already  been  stated  that  the  sodium  and  potassium  salts  of 
acids  and  the  chlorides  and  nitrates  of  bases  are  dissociated  to  such 
a  degree  that  the  equivalent  conductance  at  infinite  dilution  K*, 
is  experimentally  determinable.  By  subtraction  of  the  known 
velocity  of  migration  of  the  sodium,  potassium,  nitrate,  or  chlorine 
ion,  as  the  case  may  be,  from  this  value  of  K*,  the  velocity  of 
the  migration  of  the  other  ion  of  the  compound  is  obtained  (see 
page  106). 

Through  a  stoichiometrical  comparison  of  the  numbers  represent- 
ing the  migration  velocities  of  the  individual  ions,  certain  relations 
have  been  discovered,  some  of  which  will  be  mentioned.  These  are 
taken  from  the  comprehensive  work  of  Bredig.8 

The  migration  velocity  of  ions  of  elementary  substances  is  a 
periodic  function  of  the  atomic  weight.  It  increases  with  increas- 
ing atomic  weight  in  any  series  of  related  elements.  In  these  cases, 
the  rule  applies  that  considerable  differences  occur  with  the  first  two 
or  three  members  of  each  series.  Moreover,  similar  or  related  ele- 
ments whose  atomic  weights  are  greater  than  thirty-five  migrate 
with  nearly  the  same  velocity.  These  statements  are  illustrated  by 
the  following  results  obtained  at  18°  t.  See  also  the  values  given 
on  page  93. 

1  For  further  relationships  between  the  chemical  constitution  and  the  affinity 
constants,  see  Wegscheider,  Wien.  Monatshefte,  23,  287  (1902). 

2  Walker,  Ztschr.  phys.  Chem.,  32,  137  (1900). 
8  Ztschr.  phys.  Chem.,  13,  191  (1894). 


CONDUCTANCE   OF   ELECTROLYTES 


117 


ELEMENT 

ATOMIC  WEIGHT 

Ue 

ELEMENT 

ATOMIC  WEIGHT 

tro 

Lithium 

7 

33.4 

Fluorine 

19 

46.6 

Sodium 

23 

43.5 

Chlorine 

36 

65.4 

Potassium 

39 

64.7 

Bromine 

80 

67-6 

Rubidium 

85 

67.6 

Iodine 

127 

66.4 

Caesium 

133 

68.2 

For  complex  ions  the  following  principles  have  been  established. 
Isomeric  ions  migrate  with  the  same  velocity,  as  is  evident  from 
the  following  values  : l  — 


ISOMERIC  ANIONS 

Uo 

ISOMERIO  CATIONS 

Uc 

j  Butyric 

30.7 

(  Propyl  ammonium 

40.1 

(  Isobutyric 

30.9 

(  Isopropyl  ammonium 

40.0 

(  Cinnamic 

27.3 

{  Chinolin  methylium 

36.5 

(  Atropic 

27.1 

|  Isochinolin  methylium 

36.6 

Similar  changes  in  the  composition  of  analogous  ions  produce 
changes  in  the  same  direction  in  the  respective  migration  velocities. 
The  magnitude  of  these  changes  does  not  remain  constant  for  suc- 
cessive changes  in  the  composition,  but  decreases  with  decreasing 
migration  velocity.  In  other  words,  as  the  number  of  atoms  are  in- 
creased in  an  ion,  or  as  an  ion  becomes  more  complicated  in  its 
structure,  its  migration  velocity  decreases,  tending  towards  the  gen- 
eral minimum  value  for  univalent  anions  and  cations,  namely,  about 
seventeen  to  twenty  reciprocal  Siemens  units.  A  glance  at  the  fol- 
lowing values  will  make  this  more  evident :  — 


ION 

SYMBOL 

VELOCITY 

DIFFERENCE  PEB  CII, 

Ammonium 

NH4 

70.4 

Dimethyl  ammonium 

NH2(CH3)2 

50.1 

2(10.2) 

Diethyl  ammonium 

NH2(C2H6)2 

36.1 

2(7.0) 

Dipropyl  ammonium 

NH2(C3H7)2 

30.4 

2(2.9) 

Dibutyl  ammonium 

NH2(C4H9)2 

26.9 

2(1.8) 

Diainyl  ammonium 

NH2(C6Hn), 

24.2 

2(1.4) 

In  analogous  series  of  anions  and  cations  of  the  same  valence, 
the  migration  velocity  is  diminished  :  — 

1  These  values  have  been  taken  directly  from  the  article  by  Bredig,  and  are 
expressed  in  reciprocal  Siemens  units.     Temperature  =  25°  t 


118 


A  TEXT-BOOK  OF   ELECTRO-CHEMISTRY 


a.  By  the  addition  of  hydrogen,  carbon,  nitrogen,  chlorine,  and 
bromine. 

b.  By  the  replacement  of  hydrogen  by  chlorine,  bromine,  iodine, 
etc. 

In  general,  the  more  complicated  the  ion,  the  lower  is  its  migra- 
tion velocity.  Accordingly,  a  polymeric  ion  moves  more  slowly 
than  a  simple  one. 

The  effect  of  added  atoms  or  atom-groups  on  the  migration  velocity 
of  an  ion  is  often  obscured  by  the  effect  of  the  constitutional  dif- 
ferences. Thus  metameric  ions,  although  of  the  same  composition, 
migrate  with  different  velocities  because  of  their  different  constitu- 
tions. In  general,  in  the  case  of  such  organic  cations,  the  migration 
velocity  increases  with  the  degree  of  symmetry,  as,  for  example,  in 
passing  from  the  primary  form  to  the  secondary,  the  secondary  to 
the  tertiary,  etc.  This  is  illustrated  by  the  values  for  the  cations  of 
the  series  of  bases  given  in  the  following  table :  — 


FORM 

ION 

SYMBOL 

VELOCITY 

Primaiy 
Secondary 

Xy-lidine 
Ethyl  aniline 

C8H12N 
C8H12N 

30.0 
30.5 

Tertiary 

f  Dimethyl  aniline 
1  Collidine 

C8H12N 

C8H12N 

33.8 
34.8 

Quaternary 

f  Pecoline  ethylium 
I  Lutidine  methylium 

C8H12N 
C8H12N 

35.1 
35.2 

Thus  the  effect  of  added  atoms  or  atom-groups  on  the  additivity, 
particularly  in  the  case  of  cations,  is  often  destroyed  by  the  opposing 
influences  of  such  constitutional  differences.  Indeed,  the  direction 
of  the  additive  change  may  even  be  reversed  through  over  compen- 
sation by  the  constitutional  changes,  as  in  the  following  case :  — 


ION 

SYMBOL 

VELOCITY 

Triethyl  ammonium 
Methyl-triethyl  ammonium 

(C2H5)3  =  N-H 
(C2H6)3  =  N-CH3 

32.6 
34.4 

In  spite  of  the  fact  that  the  latter  ion  contains  one  CH2  group 
more  than  does  the  former,  no  retardation,  but,  on  the  contrary,  an 
acceleration,  of  the  migration  velocity  takes  place. 


CONDUCTANCE  OF  ELECTROLYTES 


In  the  case  of  the  migration  velocity  of  polyvalent  ions  of  organic 
acids,  Wegscheider1  has  called  attention  to  the  following  note- 
worthy regularities :  — 

The  ratio  of  the  migration  velocities  of  bivalent  and  univalent  ions 
containing  the  same  number  of  atoms  is  approximately  equal  to  a 
constant  value  (1.78).  The  same  also  holds  true  for  the  ratio  of  the 
migration  velocities  of  bivalent  and  univalent  ions  when  the  latter 
contain  one  atom  more  than  the  former.  In  this  case  the  same  acid 
is  formed  from  the  bivalent  and  from  the  corresponding  univalent 
ion  and  the  value  of  the  ratio  is  1.81.  The  same  relationship  holds 
approximately  for  inorganic  acids,  as  follows  :  — 


BIVALENT  ION 

r<* 

UNIVALENT  ION 

v'a 

l"a  -T-  u'a 

HPO/' 

55.0 

H2P04' 

33.5 

1.64 

HAsO4" 

64.6 

H2As(V 

31.7 

1.72 

These  relations  are  also  of  interest  theoretically.  It  is  a  natural 
assumption  that  the  resistance  encountered  by  a  moving  ion  is  in- 
dependent of  the  number  of  electrical  charges  carried  by  the  ion. 
Furthermore,  since  the  force  driving  the  ion  is,  in  the  same  electrical 
field,  proportional  to  the  electrical  charges  on  the  ion,  it  would  be 
expected  that  the  migration  velocity  of  an  ion  would  be  doubled  if 
to  its  first  charge  another  be  added.  However,  as  has  been  seen, 
observation  is  not  entirely  in  agreement  with  this  conclusion. 
Hence  we  must  conclude  that  the  resistance  opposing  the  movement 
of  an  ion  is  influenced  by  the  extra  charge  upon  the  ion.  To  ex- 
plain this,  it  may  be  conceived  that  the  volume,  and  consequently 
the  frictional  resistance,  of  the  ion  is  increased  by  the  mutual  repel- 
lent action  of  the  two  charges  of  the  same  kind. 

As  the  valence  becomes  higher  and  higher,  the  effect  of  the  extra 
charge  on  the  ion  becomes  less  and  less.  In  the  case  of  ferro-  and 
ferri-cyanide  ions  it  is  practically  zero.  Their  migration  velocities 
are  89.6  and  90.3,  respectively. 

Absolute  Velocities  of  the  Ions. —  By  the  procedure  given  by 
Kohlrausch,  it  is  possible  to  calculate  the  velocity  in,  centimeters  per 

second  ( — - }  with  which  the  individual  ions  are  driven  through  an 
\sec.y 

aqueous  solution  under  the  influence  of  a  given  potential  gradient,  or 
potential  fall,  per  centimeter.     For  the  sake  of  simplicity  let  us  con- 

1  Sitzungsber.  d.  K.  Ak.  d.  Wiss.  Wien.  Math.-naturw.  Kl.t  61,  11  b,  May, 
1902.  Units  =  Siemens;  temperature  =  25°. 


120  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

sider  two  platinum  electrodes,  one  centimeter  apart,  with  one  equiva- 
lent of  negative  and  one  of  positive  ions  between  them.  Let  the  fall 
in  potential  from  one  electrode  to  the  other  be  one  volt.  If,  under 
these  circumstances,  exactly  0.001  Q  (o,=  96,540)  coulombs  of  elec- 
tricity pass  through  a  cross  section  of  the  solution  in  one  second, 
and  if  the  positive  and  negative  ions  migrate  with  the  same  velocity, 
then  each  ion  travels  through  a  distance  of  0.0005  centimeter  dur- 
ing this  time,  or  possesses  the  velocity  0.0005.  Since  0.001  Q 
coulombs  pass  though  the  cross  section,  0.001  of  an  equivalent  of 
an  ion  separates  at  each  electrode.  Moreover,  0.001  of  an  equivalent 
of  ions  must  pass  through  every  cross  section  of  the  solution,  of  which 
quantity  0.0005  of  an  equivalent  are  positive,  going  toward  the 
cathode,  and  0.0005  negative,  going  toward  the  anode.  Therefore 
0.0005  of  an  equivalent  of  ions  is  brought  up  to  each  electrode.  In 
other  words,  the  ions,  which  at  the  beginning  of  the  electrolysis 
were  0.0005  of  a  centimeter  from  the  electrode  to  which  they  were 
to  migrate,  would  just  reach  the  electrode  in  one  second.  This  gives 
the  desired  absolute  velocity  of  the  ions.  In  the  case  under  con- 
sideration, the  sum  of  the  distances  traversed  by  the  positive  and 
the  negative  ions  in  one  second  is  equal  to  0.001  of  a  centimeter. 

The  quantity  of  electricity  which  has  passed  through  the  solution 
in  one  second  (i.e.  the  current  c  in  the  amperes)  divided  by  Q,  or 
96,540,  gives,  under  the  conditions  mentioned,  the  velocity  of  the 
ions  in  centimeters  per  second,  or,  otherwise  expressed, 

u***  =  Velocity  of  the  ions  in  centimeters  per  second.        (a) 


Thus  in  the  above  case, 

'     A  =  0.001  centimeter  per  second. 
yoo4U 

The  relation  between  the  current,  fall  in  potential  between  the 
electrodes,  resistance,  and  conductance  is  as  follows  :  — 

Potential-fall 


Current  = 
and  t       Conductance  = 


Resistance 
1 


Resistance 
Combining  these  equations,  the  following  is  obtained :  — 

Current  =  Potential-fall  X  Conductance. 
Since  the  potential-fall  is  one  volt,  it  follows  that  — 

Current  =  Conductance  (express  in  reciprocal  ohms). 


CONDUCTANCE  OF  ELECTROLYTES 


121 


But  there  is  one  equivalent  of  the  electrolyte  between  the  two  elec- 
trodes. Therefore,  in  this  case,  the  conductance  measured  is  the 
equivalent  conductance,  and  the  above  equation  becomes  — 

Current  =  Equivalent  conductance. 

By  substituting  this  value  of  the  current  in  equation  (a),  the  follow- 
ing is  obtained :  — 


Equivalent  conductance 
96540 


Total  velocity  of  the  ions.          (6) 


If  the  two  ions  do  not  move  with  the  same  velocity,  they  share  the 
above  total  velocity  in  proportion  to  their  individual  migration 
velocities. 

A  numerical  example  will  make  this  discussion  clearer.  The 
equivalent  conductance  of  an  infinitely  dilute  solution  of  potassium 
chloride  at  18°  t  is  equal  to  130.0  reciprocal  ohms.  Hence,  according 
to  equation  b,  — 

Total  velocity  of  K*  +  Cl'  =  qe    ',  or  0.001346  cm.  per  second. 

u      64.6 

But  for  potassium  chloride,     —  =  ^~7- 

Hence  the  two  ions  K'  and  Cl'  share  the  total  velocity  in  the  ratio 
64.6 :  65.4.  Accordingly,  for  the  potential  gradient  of  one  volt  per 
centimeter, 

Velocity  of  K'  =  0.000669  cm.  per  second, 
and  Velocity  of  Clf  =  0.000677  cm.  per  second, 


in  a  solution  o*f  infinite  dilution. 

The  absolute  migration  velocities  ucao  and  ua00  of  a  number  of 
ions  at  infinite  dilution  in  water  solution  at  18°  t,  calculated  from 
the  most  recent  values  of  the  migration  velocities  expressed  in  units 
of  conductance  (see  page  93),  are  given  in  the  following  table :  — 


CATIONS 

sec. 
VELOCITY  
cm. 

AMONS 

sec. 
VELOCITY  
cm. 

K- 

0.00066,9 

Cl' 

0.000677 

NH4' 

0.000667 

N08' 

0.000640 

Na' 

0.000450 

C108' 

0.000570 

Li* 

0.000346 

OH' 

0.001802 

Ag' 

0.000559 

H* 

0.003294 

122  A  TEXT-BOOK  OF   ELECTRO-CHEMISTRY 

The  migration  velocities  of  ions  is  less  in  solutions  in  which  the 
dissociation  is  incomplete.  According  to  the  above  discussion,  the 
sum  of  the  migration  velocities  of  positive  and  negative  ions,  in 
such  solutions,  is  given  by  the  expression, 

KD 


96540' 

when  KD  represents  the  equivalent  conductance  of  the  electrolyte  in 
question  at  the  dilution  D.  Since,  in  such  cases,  only  a  portion  of 
the  electrolyte  takes  part  in  the  migration,  the  absolute  migration 
velocity  obtained  upon  the  assumption  that  the  entire  equivalent  of 
ions  migrates  is  too  small.  For  the  individual  ions,  in  sufficiently 
dilute  solutions,  the  following  equations  hold :  — 

Ua  =  ««L,  and  uc  =x(uc)ao. 

Here,  ua  and  uc  represent  the  migration  velocities  of  the  anion  and 
cation  respectively,  in  a  solution  in  whish  the  degree  of  dissociation 
is  equal  to  x. 

It  is  of  interest  to  note,  that  it  is  possible  to  verify  the  above  cal- 
culated values  of  the  absolute  migration  velocities  of  the  ions  by 
direct  experiments.  Such  experiments  have  been  carefully  carried 
out  by  Whetham,  Masson,  and  later  by  Abegg  and  Steele,1  following 
the  method  given  by  Lodge.  The  results  obtained  are  in  remark- 
able agreement  with  the  calculated  values.  In  a  preliminary  experi- 
ment, Lodge  measured  roughly  the  migration  velocity  of  hydrogen 
ions  in  the  following  manner :  He  brought  an  acid  solution  into 
contact  with  a  solution  of  sodium  chloride  made  red  with  alkaline 
phenolphthalein  and  solidified  in  gelatine  as  shown  in  the  accom- 
panying diagram  [Figure  32 J.  An  electric  current  was  then  passed 


FIG.  32 

from  the  acid  solution  through  the  salt  solution,  in  such  a  direction 
that  the  hydrogen  ions  entered  the  colored  gelatine  at  a.  As  these 
ions  slowly  penetrated  this  solution  of  sodium  chloride  in  jelly  they 

1  Ztschr.  phys.  Chem.,  11,  220  (1893);  Ztschr.  phys.  Chem.,  29,  501  (1899); 
Ztschr.  Elektrochemie,  7,  618  (1901);  Ztschr.  phys.  Chem.,  40,  699  and  737 
(1902). 


CONDUCTANCE   OF  ELECTROLYTES  123 

destroyed  the  red  color  of  the  indicator.  Hence,  by  measuring  the 
rate  of  progress  of  this  decoloration,  i.e.  the  time  required  for  the 
moving  boundary  between  the  colored  and  colorless  parts  of  the  so- 
lution to  reach  b  (a  known  distance  from  a),  Lodge  obtained  the 
actual  velocity  of  the  hydrogen  ions.  He  did  not,  however,  correctly 
interpret  his  results. 

Whetham  improved  the  method  used  by  Lodge,  and  determined  the 
migration  velocities  of  complex  copper  ions  in  ammoniacal  solution 
of  chlorine,  and  of  bichromate  (Cr2O/f)  ions.  He  placed  two  dilute 
solutions  of  the  same  specific  conductance,  one  of  which  was  color- 
less and  the  other  colored  (such  as,  for  example,  solutions  of  potas- 
sium carbonate  and  potassium  bichromate)  in  an  upright  tube,  the 
one  of  least  density  above  the  other.  If  this  is  carefully  done,  a 
sharp  boundary  may  be  obtained  between  colored  and  colorless  solu- 
tions, and,  when  an  electric  current  is  passed  through  the  solution  in 
such  a  direction  that  the  colored  ions  are  migrated  into  the  color- 
less solution,  their  velocity  may  be  obtained  by  measuring  the  rate  of 
movement  of  this  boundary.  The  fall  in  potential  per  centimeter,  or 
the  potential  gradient,  must  be  measured  at  the  same  time,  for  the 
velocity  of  the  ions  varies  directly  with  it. 

It  has  been  shown  by  Abegg  and  Steele  that  the  method  employed 
by  Whetham  is  also  applicable  to  solutions,  which,  although  color- 
less, refract  a  beam  of  light  to  different  degrees,  thus  making  it  pos- 
sible to  follow  the  movement  of  the  boundary  between  the  two 
solutions.  They  determined  the  migration  velocity  of  various  ions 
at  different  dilutions  of  the  electrolyte  used,  and  found  that  the 
results  obtained  agree  well  with  the  requirements  of  the  theory. 
As  the  dilution  increases,  the  migration  velocity  increases  and 
approaches  the  values  calculated  for  infinite  dilution. 

In  a  way  these  experiments  on  the  migration  velocities  are  a  con- 
tinuation and  extension  of  those  performed  by  Davy  and  described 
on  page  38.  Davy  was,  however,  prevented  from  attaining  the 
real  object  of  them  by  erroneous  assumptions  regarding  ions. 

In  this  connection  it  may  be  mentioned  that  Whitney  and  Blake  l 
found  that  negative  colloidal  suspensions  of  gold,  platinum,  ferric- 
ferrocyanide,  and  a  suspension  of  microscopic  quartz  particles, 
possess  an  initial  velocity  of  migration  of  0.0004  to  0.0005  centi- 
meter per  second,  i.e.  nearly  equal  to  that  of  C103f  ions. 

Electrolytic  Frictional  Resistance.  —  Having  calculated  the  abso- 
lute migration  velocities  of  the  ions,  the  frictional  resistance,  or  the 

1  J.  Am.  Chem.  Soc.,  26,  1339  (1904). 


124  A   TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

force  required  to  drive  them  through  a  solution,1  is  easily  obtained. 
The  mechanical  energy  or  work  expended  is  given  by  the  equa- 
tion, 

Em  or  Wm  =  Force  x  Distance. 

If  the  force  required  to  drive  one  equivalent  of  a  given  kind  of 
ions  through  a  solution  with  a  unit  velocity  of  one  centimeter  per 
second  is  F,  then  the  force  required  to  drive  the  same  quantity  with 
a  velocity  U  centimeters  per  second  is  equal  to  FU.  By  substitu- 
tion of  these  values  in  the  above  equation,  we  obtain 

Em  or  Wm  =  FU  X   U. 

The  electrical  energy  EeJ  or  electrical  work,  is  represented  by  the 
equation, 

Ee  or  We  ==  Volts  X  Coulombs  =  Volts  x  Amperes  x  Seconds. 

By  substitution  of  the  numerical  values  in  this  equation,  the 
following  is  obtained :  — 

E.  or  We  =  1  x  96540  U=  984515  *7kgm.  cm. 
By  placing  the  mechanical  work  equal  to  the  electrical  work,  — 

FU  x  U=  984515  U; 
p=  984514 
U 

If  one  equivalent  of  ions  be  represented  by  Eq,  then  for  one  gram 
of  the  ions, 

j,=  984515 
UxEq 

The  value  of  this  force  for  hydrogen  ions  in  a  solution  in  which 
complete  dissociation  has  taken  place  has,  for  example,  been  calcu- 
lated to  be  equal  to  299  x  106  kilograms.  This  enormous  value  of 
the  force  is  in  agreement  with  the  results  of  other  calculations,  and 
may  be  accounted  for  by  the  extreme  state  of  division  of  the  gram 
of  hydrogen  ions.  According  to  the  calculations  made  by  Planck, 
one  atomic  weight  in  grams  of  an  elementary  substance  consists  of 
0.617  x  1084  atoms.  One  atom  of  hydrogen,  then,  weighs  1.63  x  10~24 
grams,  and  is  charged  with  15.65  x  10"20  coulombs  of  electricity. 
This  charge  may  be  considered  as  an  elementary  quantity  of  elec- 
tricity. 

1  Wied.  Ann.  50,  385  (1893). 


CONDUCTANCE  OF  ELECTROLYTES  125 

The  Limited  Applicability  of  the  Ostwald  Dilution  Law.    Empirical 

Rules. —  It  is  evident  from  a  consideration  of  its  derivation  that  the 
equation, 

— 1>  TS- 


which  is  an  expression  of  Ostwald's  Dilution  Law,  is  applicable  only 
in  the  case  of  binary  electrolytes.  From  the  fact  that  slightly  dis- 
sociated acids  of  other  types,  such  as  the  di-  and  tri-basic  acids,  be- 
have on  dilution  according  to  the  requirements  of  the  above  equation, 
it  follows  that,  at  first,  only  one  hydrogen  atom  separates  as  a  posi- 
tive ion,  leaving  the  others  combined  in  the  univalent  negative  ion, 
as  represented  in  the  equation, 


On  continued  dilution,  the  other  hydrogen  atoms  begin  to  separate 
appreciably  in  the  form  of  ions,  and  simultaneously  the  negative 
ions  from  which  they  separate  increase  their  valences.  This  is  evi- 
dent from  the  equation, 


Experiments  have  not  been  made  to  determine  dissociation  con- 
stants for  tertiary  electrolytes  ;  moreover,  as  will  be  seen  from  the 
following  discussion,  they  probably  would  not  be  very  successful. 

It  has  been  found  that  the  above  dissociation  equation  does  not 
hold  for  highly  dissociated  binary  electrolytes,  such  as  the  neutral 
salts,  the  mineral  acids,  and  the  inorganic  bases.  Consequently  the 
relations  formerly  deduced  for  highly  dissociated  electrolytes  from 
the  dissociation  equation  can  only  be  considered  as  mere  approxima- 
tions. Regarding  the  cause  of  this  inapplicability  of  the  equation 
opinions  still  differ  widely.1 

The  following  empirical  equation  holds  well  over  a  wide  range  of 
temperature,  for  salts  which  dissociate  into  monovalent  or  into 
monovalent  and  polyvalent  ions,  at  concentrations  between  the 
values  0.001  and  0.2  normal:  — 

=  Constant, 

where  (7  represents  the  concentration  of  the  solution,  x  the  degree  of 
dissociation,  and  n  a  numerical  value  which  varies  from  1.43  to  1.56. 

1  See,  for  example,  Jahrbuch  d.  Elektrochemie,  8,  102  (1902),  and  A.  A. 
Noyes,  Technology  Quarterly,  17,  No.  4  (December,  1904). 


126  A   TEXT-BOOK   OF   ELECTRO-CHEMISTRY 

For  salts  which  dissociate  into  monovalent  or  into  monovalent 
and  polyvalent  ions,  the  following  simpler  equations  hold  between 
the  concentrations  0.0005  and  1  normal  :  — 

1  —  x  =  Constant  x  C7*» 
or  1  —  x  =  Constant   x   (Cx)*- 

Hence  the  undissociated  part  of  a  salt,  as  determined  by  conduc- 
tivity measurements,  is  proportional  to  the  cube  root  of  the  total  concen- 
tration of  the  salt,  or  to  the  cube  root  of  its  ion  concentration. 

An  empirical  rule,  expressing  the  change  of  equivalent  conduc- 
tance of  neutral  salts  with  the  dilution,  has  been  discovered  by  Ost- 
wald.  By  means  of  this  rule,  it  is  possible  to  calculate  the  basicity 
of  an  acid,  and  also  the  value  of  its  equivalent  conductance  at 
infinite  dilution.  It  is  of  great  service  in  the  case  of  salts  which 
undergo  hydrolysis  to  a  large  extent  at  moderately  high  dilutions.1 
Ostwald  found  that  the  equivalent  conductance  of  the  sodium  salts 
of  all  monobasic  acids  increases  ten  units,2  of  all  dibasic  acids 
twenty  units,  and  of  all  tribasic  acids  thirty  units,  between  the 
equivalent  dilutions  32,000  and  1,024,000  cubic  centimeters.  If  the 
increase  in  equivalent  conductance  between  these  two  dilutions  be 
represented  by  A,  and  the  basicity  of  the  acid  by  B,  then  the  rule  is 
expressed  by  the  equation, 


The  following  values  for  A  and  —  have  been  obtained  :  — 


SODIUM  SALT  OP 

A 

_& 

10 

Nicotinic  acid     .        .-       .        .        .        .        . 
Chinoline  acid    .        .        .        .        .        .        „ 

10.4 
19.8 

1.04  (approx.  1) 
1.98  (approx.  2} 

Py  ri  dine  tricarbonic  acid    .        «        *        .        ^  ' 

31.0 

3.10  (approx.  3) 

Pyridine  tetracarbonic  acid        . 
Pyridine  pentacarbonic  acid       .... 

40.4 
50.1 

4.04  (approx.  4) 
5.01  (approx.  5) 

On  the  other  hand,  from  the  value  of  this  difference  A  of  an  acid 
of  known  basicity,  an  indication  may  be  obtained  of  the  presence  or 
absence  of  hydrolysis.  In  the  case  of  a  salt  of  a  very  weak  acid,  as, 
for  example,  potassium  cyanide,  as  the  dilution  increases  the  cyanide 
ions  combine  to  a  certain  extent  with  the  hydrogen  ions  of  the  water 

1  Ztschr.phys.  Chem.,  1,  109  and  529  (1887)  ;  2,  901  (1888). 

2  The  values  used  on  pages  126  and  127  are  expressed  in  reciprocal  Siemens 
units. 


CONDUCTANCE  OF  ELECTROLYTES 


127 


(see  next  section),  forming  undissociated  hydrocyanic  acid.  The 
cyanide  ions  which  thus  disappear  are  replaced  by  hydroxyl  ions 
from  the  water.  This  reaction  between  the  salt  and  water,  or  the 
hydrolysis,  is  represented  by  the  equation, 

K*  +  CN'  +  H'  +  OH'  (from  water)  ^r  HCN  +  K'  +  OH'. 

The  final  result,  then,  of  the  dilution  is  that  the  number  of  hy- 
droxyl ions,  instead  of  that  of  the  cyanide  ions,  has  been  increased. 
Since  the  migration  velocity  of  hydroxyl  ions  is  far  greater  than 
that  of  cyanide  ions,  the  equivalent  conductance  of  potassium  cya- 
nide increases  more  rapidly  with  increasing  dilution  than  would  be 
the  case  in  the  absence  of  hydrolysis,  and,  consequently,  the  value 
of  the  above  difference  A  is  abnormally  great.  An  analogous  pro- 
cess takes  place  in  the  case  of  a  salt  of  a  strong  acid  and  a  weak 
base,  with  the  exception  that,  instead  of  an  undissociated  acid  and 
hydroxyl  ions,  an  undissociated  base  and  rapidly  migrating  hydro- 
gen ions  are  formed. 

Finally,  for  neutral  salts  which  dissociate  to  a  large  degree  the 
following  relation  has  been  found  to  exist :  — 


vaxvc  x 


or 


when  K^  is  nearly  equal  to  K^.  In  these  equations,  v0  and  vc  rep- 
resent the  valency  of  the  anion  and  cation,  respectively,  and  K  is  a 
constant  for  all  electrolytes  which  is  dependent  on  the  dilution. 
Having  determined  the  value  of  the  constant  at  different  dilutions 
once  for  all  for  a  single  electrolyte  of  known  equivalent  conductance 
at  infinite  dilution,  it  is  possible  to  calculate  the  latter  equivalent 
conductance  for  any  other  electrolyte  from  a  knowledge  of  the  va- 
lences of  its  ions  and  its  equivalent  conductance,  at  any  dilution  for 
which  the  constant  is  known.  If  the  product  va  X  vc  x  K  is  repre- 
sented by  pD,  when  D  is  the  equivalent  dilution  of  the  solution  in 
cubic  centimeters,  then  v 

K*  =  PD  +  £/>• 


vaxvc 

#6400 

#12,800 

#256,000 

#512,000 

#1,024,000 

1 

11 

8 

6 

4 

3 

2 

21 

16 

12 

8 

6 

3 

30 

23 

17 

12 

8 

4 

42 

31 

23 

16 

10 

5 

53 

39 

29 

21 

13 

6 

(60) 

48 

36 

25 

16 

128  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

In  the  preceding  table  are  given  the  values  found  by  Bredig  foi 
pD  for  different  values  of  the  product  of  the  valencies  of  the  ions 
and  for  different  dilutions  at  25°  t. 

The  following  relation,  which  was  first  noted  by  Bodlander  and 
Storbeck,1  can  often  be  conveniently  used  :  — 


when  a?!+n  represents  the  degree  of  dissociation  of  a  salt  which  forms 
univalent  and  n-valent  ions,  and  a^+1  that  of  a  salt  which  dissociates 
only  into  univalent  ions.  This  equation  holds  when  salts  of  the 
same  base  are  compared  at  the  same  equivalent  concentration. 
Thus,  if  the  salts  potassium  chloride  and  potassium  ferrocyanide 
be  compared  at  the  same  dilution, 

~  X  Ed- 


it may  be  mentioned,  in  conclusion,  that  the  fact,  already  noticed, 
that  the  migration  velocities  are  dependent  chiefly  upon  the  number 
of  atoms  contained  in  the  ion,  may  be  used  in  order  to  obtain  the  value 
of  the  equivalent  conductance  of  compound  ions  at  infinite  dilution. 
If  it  is  known,  for  example,  that  the  anion  of  a  certain  acid  contains 
eighteen  atoms,  its  equivalent  conductance  at  infinite  dilution  may 
be  considered  to  be  equal  to  that  of  another  anion  of  the  same  num- 
ber of  atoms,  without  introducing  any  considerable  error.  The  same 
reasoning  may  be  applied  to  the  temperature  coefficients  of  the  con- 
ductance of  individual  ions. 

The;  Conductivity  and  Degree  of  Dissociation  of  Water.  —  Thus  far 
it  has  been  assumed  that  the  observed  conductance  of  aqueous  solu- 
tions is  due  entirely  to  the  dissolved  substance,  or  solute,  and  that  the 
water  itself  possesses  no  conductance.  Strictly  speaking,  however,  this 
is  not  true,  for  the  water  dissociates,  though  to  an  extremely  slight 
degree,  into  hydrogen  and  hydroxyl  ions  which  take  part  in  the  con- 
ductance with  whatever  other  ions  there  may  be  present.  For  all 
ordinary  measurements  of  the  conductance  of  solutions,  the  conduc- 
tance of  the  pure  water  is  entirely  inappreciable.  On  the  other  hand, 
the  impurities  usually  found  in  water,  such  as  traces  of  salts,  acids, 
or  bases,  which  are  removed  only  with  great  difficulty,  may  cause  a 
considerable  error  in  the  conductance  determinations  in  the  case 
of  dilute  solutions.  When  such  solutions  are  being  investigated, 
it  is  necessary  to  determine  the  conductivity  of  the  water  used, 
and  to  apply  the  value  obtained  as  a  correction  in  the  final  results. 

For  a  number  of  years  Kohlrausch  expended  a  great  deal  of  effort 

i  Ztschr.  anorg.  Chem.,  39,  201  (1904). 


CONDUCTANCE  OF  ELECTROLYTES        129 

in  determining  the  actual  conductance  of  pure  water.  For  water 
which  was  prepared  and  purified  with  the  greatest  care,  he  found 
the  following  values  for  the  specific  conductance,  or  conductivity : l  — 


TEMPERATURE  (t) 

SPECIFIC  CONDUCTANCE 

0° 

0.01    x  10-« 

18° 

0.038  x  10-« 

50° 

0.17    x  10-« 

"  One  millimeter  of  this  water  at  0°  possessed  a  resistance  equal 
to  that  of  forty  million  kilometers  of  copper  wire  of  the  same  sec- 
tional area,  or  a  length  of  wire  capable  of  encircling  the  earth  a 
thousand  times." 

For  reasons  not  necessary  to  give  here,  it  is  probable  that  this 
experimentally  found  value  is  very  near  the  actual  value  of  the  con- 
ductivity of  pure  water.  Given  this  value,  the  degree  of  dissociation 
of  water  can  easily  be  calculated. 

The  above  table  states  that  the  conductance  of  a  centimeter  cube 
of  this  water  at  18°  is  equal  to  0.038  x  10~6  reciprocal  ohms.  Con- 
sequently the  conductance  of  one  liter  of  it  between  electrodes  one 
centimeter  apart  is  103  times  greater  than  this  value,  or  equal  to 
0.038  X  10  3.  If  there  were  present,  in  this  quantity  of  the  water, 
one  equivalent  of  hydrogen  and  one  of  hydroxyl  ions,  the  conduc- 
tance would  have  been  equal  to  492  reciprocal  ohms,  since,  as  has 
already  been  explained,  the  conductance  of  one  equivalent  of  hydrogen 
ions  between  electrodes  one  centimeter  apart  is  equal  to  318,  and  that 
of  the  same  quantity  of  hydroxyl  ions,  under  the  same  conditions, 
174  reciprocal  ohms.  If  the  conductance  had  been  found  to  be  equal 
to  492  reciprocal  ohms,  the  water  would  have  been  1/1  normal  in 
respect  to  hydrogen  and  hydroxyl  ions.  It  was,  however,  found  to 
be  0.038  x  10~3  reciprocal  ohms.  Hence  the  concentration  of  these 

ions  in  the  water  is  equal  to  — ,  or  0.77  X  10~7,  normal,  or, 

otherwise  expressed,  one  gram  of  hydrogen  and  seventeen  grams  of 
hydroxyl  ions  are  present  in  about  thirteen  million  liters  of  water. 

Supersaturated  Solutions.  —  The  idea  has  been  prevalent  for  a  very 
long  time,  and  has  not  even  yet  disappeared,  that  supersaturated 
solutions  must  behave  in  a  manner  characteristically  different  from 
saturated  and  unsaturated  solutions.  Conductivity  measurements 

1  Kohlrausch  and  Heydweiller,  Ztschr.phys.  Chem.,  14,  317  (1894). 


130  A  TEXT-BOOK  OF   ELECTRO-CHEMISTRY 

have,  however,  shown  that  supersaturated  solutions  possess  no 
peculiar  properties  not  manifested  by  other  solutions.  If,  for  exam- 
ple, the  conductivity  of  a  solution  of  a  salt,  whose  solubility  increases 
rapidly  with  rising  temperature,  be  measured  at  a  series  of  tempera- 
tures varying  from  those  at  which  the  solution  is  supersaturated  to 
those  at  which  it  is  unsaturated,  it  will  be  found  that  the  change  of 
conductivity  with  the  temperature  is  perfectly  regular  throughout. 
If  the  results  thus  obtained  be  plotted  on  a  coordinate  system,  it  will 
be  found  that  a  regular  curve  results  which  gives  no  evidence  of  the 
passage  of  the  solution  from  the  supersaturated  to  the  saturated,  and 
finally  to  the  unsaturated,  state.  If  supersaturated  solutions  were 
qualitatively  different  from  ordinary  solutions  a  sudden  change  in 
the  slope  of  the  curve  would  have  been  observed  at  the  saturation 
temperature. 

Temperature  Coefficient.  —  According  to  Kohlrausch,  the  change 
in  conductivity  with  the  temperature  is  nearly  linear,  and  may  be 
expressed,  often  between  wide  temperature  limits,  by  the  following 
equation  :  — 


In  this  equation  K2  and  KJ  are  the  conductivities  at  the  temperatures 
t2  and  tt  respectively  ;  (AKIO)  is  the  temperature  coefficient,  which 
gives  the  change  of  conductance,  expressed  as  a  fraction  of  the 
conductivity,  KO,  at  a  given  temperature,  for  a  change  in  temperature 
of  one  degree.  Generally  18°  is  chosen  as  the  given  temperature. 
The  above  equation  may  then  be  written  as  follows  :  — 


It  has  been  found  that,  in  the  case  of  all  well  investigated  elec- 
trolytes which  dissociate  to  a  high  degree  into  univalent  ions,  the 
temperature  coefficient  is  the  greater  the  smaller  the  value  of 
the  equivalent  conductance.  From  this  fact  Kohlrausch  deduced 
the  following  principle  :  J  The  temperature  coefficient  of  univalent 
ions  is  a  function  of  their  mobility.  That  is  to  say,  the  greater  the 
migration  velocity  the  less  is  the  temperature  coefficient.  It  follows 
from  this  that  the  ratio  of  the  mobilities  of  any  two  ions  approaches 
unity  as  the  temperature  increases,  which  is  in  agreement  with  the 

1  Sitzungsber.  der  konigl.  Pr.  Akad.  der  Wiss.  Physik.  Mathem.  Kl.,  26,  572 
(1902). 


CONDUCTANCE   OF   ELECTROLYTES 


131 


statement  made  on  page  76  that  the  transference  numbers  approach 
the  value  0.5  with  increasing  temperature.1 

The  magnitude  of  the  temperature  coefficient  at  ordinary  tem- 
peratures is  shown  by  the  values  for  dilute  solutions  given  in  the 
following  table :  — 


DILUTE  SOLUTB 

TEMPERATURE  COEFFICIENT 

Salts 
Acids 


0.020  to  0.023 
0.009  to  0.016 
0.019  to  0.020 


A  temperature  difference  of  one  degree  thus  changes  the  value  of 
the  conductivity  by  from  one  to  two  and  a  half  per  cent,  from 
which  the  importance  of  making  conductivity  measurements  only  at 
constant  temperatures  is  at  once  evident. 

As  the  concentration  of  the  solution  is  increased,  the  temperature 
coefficient  at  first  decreases  and  then  increases  slightly. 

With  the  aid  of  the  expression, 

u,  =  ulfio  (1  +  a  (t  -  18)  +  p  (t- 18)2), 

the  migration  velocity  of  an  ion  at  temperatures  not  far  from  18°  t, 
u,,  can  be  calculated  if  the  values  a,  (3,  and  u180  be  known  for  this 
ion.  A  table  of  values  of  ulgo  is  given  on  page  93.  In  the  follow- 
ing table  are  given  the  values  of  a  and  ft  calculated  by  Kohlrausch 2 
from  experimental  data :  — 


ION 

a 

/3 

ION 

a 

ft 

H 

0.0154 

-  0.000033 

F 

0.0232 

+  0.000094 

OH 

179 

+             08 

10. 

233 

096 

N08 

203 

47 

C2H8O2 

236 

101 

I 

206 

52 

£Ba 

239 

106 

C108 

207 

54 

*Cu 

240 

107 

Cl 

215 

67 

*Pb 

244 

114 

Rb 

217 

69 

Na 

245 

116 

K 

220 

75 

*Mg 

255 

132 

NH4 

223 

79 

£Zn 

256 

133 

}S04 

226 

84 

Li 

261 

142 

Ag 

231 

93 

*C08 

269 

155 

iSr 

231 

93 

1  Further  particulars  may  be  found  in  the  recent  comprehensive  investigation 
of  Jones  and  West,  Am.  Chem.  «/.,  34,  357  (1905). 

2  Sitzungsber.,  42,  1031  (1901). 


132  A   TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

It  may  further  be  mentioned  that  conductivity  measurements 
have  recently  been  carried  out  at  very  high  temperatures  (to  above 
3000).1 

If  it  be  imagined  that  the  ions  in  moving  through  a  solution  must 
overcome  a  certain  frictional  resistance,  the  existence  of  a  certain 
parallelism  between  the  change  of  the  internal  friction  or  viscosity 
and  that  of  electrical  conductance  of  many  solutions  with  the  tem- 
perature becomes  comprehensible.  There  is  not,  however,  a  strict- 
proportionality  between  the  two  properties. 

Finally,  it  is  a  noteworthy  fact  that,  in  contrast  to  conductors  of 
the  first  class,  the  temperature  coefficient  of  the  conductance  of  electro- 
lytes is  nearly  always  positive.  In  other  words,  the  conductivity  of 
an  electrolyte  nearly  always  increases  with  increasing  temperature. 
The  conductance  of  a  solution  depends  both  upon  the  migration  veloc- 
ity and  the  number  of  the  ions  contained  in  it.  The  migration  velocity 
itself  depends  upon  the  magnitude  of  the  friction  which  the  ions  en- 
counter in  the  water.  Since  the  internal  friction  of  the  water  dimin- 
ishes with  rising  temperature,  it  may  be  assumed  that  the  friction 
of  the  ions  also  diminishes  and,  as  a  consequence,  the  conductance 
increases.  This  must  be  the  case  especially  with  salt  solutions, 
since,  owing  to  the  high  degree  of  dissociation,  the  increase  in  con- 
ductance with  rising  temperature  cannot  be  ascribed  to  any  consid- 
erable extent  to  a  change  in  the  degree  of  dissociation.  According 
to  this  conception  of  the  temperature  effect,  a  decrease  in  conduc- 
tance with  rising  temperature  can  only  take  place  when  the  effect  of 
the  diminution  in  the  number  more  than  compensates  the  effect 
of  the  increased  mobility  of  the  ions.  In  other  words,  with  rising 
temperature  a  decrease  in  dissociation  of  the  electrolyte  must  in 
this  case  take  place.  To  many  this  conclusion  may,  at  first  sight, 
seem  unjustifiable,  in  view  of  the  fact  that  from  the  kinetic  gas 
theory  it  would  be  expected  that  with  rising  temperature  an  increase 
in  dissociation  would  take  place.  According  to  the  laws  and  princi- 
ples of  energetics  however,  this  is  not  at  all  the  case,  but,  on  the 
contrary,  it  may  be  predicted  that  in  certain  cases  an  increase  in 
temperature  must  be  accompanied  by  a  decrease  in  dissociation. 
The  principle  of  energetics  applying  to  such  changes  may  be  stated 
as  follows :  — 

If  one  of  the  factors  determining  the  equilibrium  of  a  system  be 
varied  in  one  direction,  the  equilibrium  undergoes  a  change  which, 
if  it  took  place  of  itself,  would  be  accompanied  by  a  variation  of  this 
factor  in  the  opposite  direction. 

i  A.  A.  Noyes  and  W.  D.  Coolidge,  Ztschr.  phys.  Chem.,  46,  323  (1903). 


CONDUCTANCE  OF  ELECTROLYTES  133 

If  the  factor  temperature  be  varied  in  a  chemical  system,  the 
above  principle  may  be  restated  as  follows:  — 

If  a  chemical  system  at  equilibrium  be  heated,  the  equilibrium  is  dis- 
placed in  that  direction  in  which  heat  is  absorbed. 

Consider,  for  example,  a  saturated  solution  of  a  substance  in  con- 
tact with  the  solid  substance.  If  the  solution  be  heated,  according 
to  the  principle  of  energetics,  that  change  will  take  place  which  is 
accompanied  by  an  absorption  of  heat,  i.e.  by  a  cooling  effect.  Con- 
sequently, if  the  substance  dissolves  (in  a  nearly  saturated  solution) 
with  an  absorption  of  heat,  more  of  it  will  go  into  solution ;  if  with 
an  evolution  of  heat,  some  of  it  will  precipitate  out  of  solution. 

In  a  similar  manner,  the  principle  may  be  applied  to  the  change 
of  the  dissociation  of  any  electrolyte  with  the  temperature.  All 
electrolytes  which  tend  to  become  less  dissociated  with  rising  tem- 
perature, and  consequently  all  electrolytes  possessing  negative 
temperature  coefficients  of  the  conductance,  must  dissociate  with  an 
evolution  of  heat,  or,  otherwise  expressed,  must  possess  a  negative 
heat  of  dissociation.  By  heat  of  dissociation  is  meant  the  heat 
effect  attending  the  union  of  ions  to  form  an  undissociated  molecule, 
and  by  positive  and  negative  heats  is  meant  respectively  the  heat 
that  is  given  off  to  or  absorbed  from  the  surroundings. 

By  means  of  direct  determinations  of  the  heat  of  dissociation,  it 
is  possible  to  test  the  correctness  of  the  above  conclusions. 

Heat  of  Dissociation.  — According  to  the  dissociation  theory,  the 
process  of  neutralization  of  a  strong  base  with  a  strong  acid  con- 
sists solely  in  the  combining  of  the  hydrogen  ions  of  the  acid  and 
the  hydroxyl  ions  of  the  base  to  form  undissociated  water  molecules. 
It  has  already  been  shown  that  the  degree  of  dissociation  of  water 
is  very  small.  Consequently  the  product  of  the  concentrations  of 
the  hydrogen  and  the  hydroxyl  ions  must  be  extremely  small.  Now 
according  to  the  law  of  mass  action,  whenever  hydrogen  and 
hydroxyl  ions  are  brought  together,  combination  must  take  place  as 
required  by  the  equation, 


Since,  in  an  aqueous  solution  the  concentration  of  the  undissociated 
water  is  very  great  compared  with  that  of  the  hydrogen  and  hy- 
droxyl ions,  it  may  be  considered  a  constant.  The  above  equation 
may  then  be  written  as  follows, 


134  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

Since  even  in  pure  water  sufficient  hydrogen  and  hydroxyl  ions 
are  always  present  to  satisfy  this  equation,  and  as  the  value  of 
this  product  cannot  be  exceeded,  it  follows  that  all  hydrogen  and 
hydroxyl  ions  brought  into  water  must  disappear.  Now  before 
mixing  an  alkali  with  an  acid  solution,  we  have  in  one  case  metal 
and  hydroxyl  ions  and  in  the  other  acid  and  hydrogen  ions,  as  may 
be  illustrated  by  sodium  hydroxide  and  hydrochloric  acid.  In  this 
case  the  following  ions  are  present  in  the  two  solutions,  respec- 
tively :  — 

Na'andOH';  H'andCl'. 

After  mixing  the  acid  and  alkali  solutions,  the  ions  of  the  metal 
and  of  the  acid  radical  are  still  present  and  free  in  the  solution, 
constituting  a  highly  dissociated  salt.  They  have  taken  no  part  in 
the  process  of  neutralization.  In  the  case  of  sodium  hydroxide  and 
hydrochloric  acid,  only  sodium  and  chlorine  ions  are  present  after 
mixing  the  two  solutions,  constituting  sodium  chloride  in  the  dis- 
solved state.  Hence  the  real  reaction  which  has  taken  place  is 
represented  by  the  equation 

H  +OH'  =  H2O. 

It  is  because  of  the  fact  that  the  ions  of  the  metal  and  those  of  the 
acid  radical  take  no  part  in  the  process  of  neutralization  that  the 
value  of  the  heat  of  neutralization  is  the  same  for  all  highly  disso- 
ciated acids  and  bases,  being  in  each  case  the  heat  of  the  union  of 
hydrogen  and  hydroxyl  ions  to  form  undissociated  water.  This 
value  for  one  equivalent  of  acid  and  base  is  13,700  calories,  at  ordi- 
nary temperatures.  Hence  the  above  equation  may  be  written  as 

follows :  — 

H'  +  OH'  =  H20  + 13700  calories, 

where  the  ions  are  present  in  equivalent  quantities. 

The  value  13,700  calories  then  really  represents  the  heat  of  dissocia- 
tion of  water. 

This  value  must  not  be  confused  with  the  heat  evolved  when 
gaseous  hydrogen  reacts  with  gaseous  oxygen  to  form  water. 

If  a  partially  dissociated  acid  be  neutralized  with  a  highly  disso- 
ciated base,  the  heat  of  neutralization  will  be  made  up  of  the  sum 
of  two  heats  of  dissociation,  namely,  that  of  water  and  that  of  the 
acid.  Representing  the  heat  of  neutralization  by  Hn,  the  degree  of 
dissociation  of  the  acid  by  «,  and  the  heat  of  the  dissociation  of 
the  acid  by  Hd,  then 

Hn  =  13700  -  (1  -  a)  Hd  calories. 


CONDUCTANCE  OF  ELECTROLYTES        135 

Hence  it  follows  that 


1  —X 

All  dissociating  acids  which  exhibit  a  greater  heat  of  neutraliza- 
tion than  13,700  calories  have  negative  heats  of  dissociation.  It  has 
actually  been  found  by  Arrhenius  l  and  later  by  Euler  that  all  acids 
which  possess  a  negative  temperature  coefficient  of  electrical  con- 
ductivity have  also  negative  heats  of  dissociation.  Such  acids 
therefore  decrease  in  dissociation  with  rising  temperature. 

Influence  of  Pressure.  —  The  influence  of  pressure  upon  the  con- 
ductivity of  electrolytes  may  be  predicted  from  the  same  reasoning 
which  explains  the  influence  of  temperature.  By  means  of  a  change 
in  pressure  a  change  may  be  produced  in  the  concentration  of  the 
solution,  the  friction  of  the  ions,  and  the  dissociation  of  the  elec- 
trolyte. Eliminating  the  change  in  concentration,  which  may  be 
applied  as  a  correction  in  the  calculation  of  the  final  results,  experi- 
ment shows  that,  in  general,  the  conductivity  of  dilute  solutions  of 
highly  dissociated  electrolytes  increases  with  increasing  pressure. 
This  may  be  ascribed  to  a  diminution  in  the  friction  of  the  ions 
with  the  water.  This  is  in  agreement  with  the  fact  that  the  inter- 
nal friction  or  viscosity  of  water  decreases  with  increasing  pressure. 
Therefore,  as  in  the  case  of  the  temperature  effect,  there  exists  here 
also  a  parallelism  between  the  change  in  conductivity  and  the  change 
in  internal  friction. 

In  the  case  of  electrolytes  which  are  but  partly  dissociated,  the 
effect  of  pressure  upon  the  degree  of  dissociation  must  also  be 
taken  into  consideration.  This  may  be  obtained  from  the  volume 
change  during  dissociation,  just  as  the  effect  of  temperature  change 
was  obtained  from  the  heat  evolved  or  absorbed  during  dissociation, 
i.e.  the  heat  of  dissociation.  If  the  formation  of  ions  is  accompa- 
nied by  a  diminution  in  volume,  then  an  increase  in  pressure  is 
accompanied  by  an  increase  in  the  degree  of  dissociation.  This  fol- 
lows from  the  law  stated  on  page  132  expressing  the  change  in  equi- 
librium caused  by  a  change  in  one  of  its  factors,  since  an  increase  in 
pressure  is  accompanied  by  a  decrease  in  volume,  and  this  change  in 
dissociation,  taking  place  of  itself,  is  accompanied  by  a  decrease 
in  volume.  As  a  matter  of  fact,  the  dissociation  of  many  moder- 
ately dissociated  acids  is  accompanied  by  such  a  decrease  in  volume  ; 
and  corresponding  to  this,  the  increase  in  volume  during  neutraliza- 
tion with  a  strong  base  is  less  for  these  acids  than  for  acids  which 

1  Ztschr.phys.  Chem.,  4,  96  (1889)  ;  9,  339  (1892). 


136  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

are  nearly  completely  dissociated.  This  is  analogous  to  the  above 
consideration  of  the  heat  of  dissociation. 

It  is  a  necessary  consequence  from  the  investigations  of  Fanjung1 
that  the  conductivity  of  such  acids  should  increase  with  rising  pres- 
sure to  a  greater  extent  than  that  of  highly  dissociated  electrolytes, 
especially  in  the  case  of  their  sodium  salts.  This  is  in  complete 
agreement  with  the  above  explanations. 

Mixed  Solutions:  Isohydric  Solutions.  Application  of  Electrical 
Conductivity  to  Chemical  Analysis.  —  If  the  conductivities  of  two 
solutions  and  of  a  mixture  of  equal  volumes  of  the  two  solutions  are 
determined  under  the  same  circumstances,  it  will  not,  in  general,  be 
found  that  the  latter  value  is  equal  to  the  average  of  the  other  two, 
excepting  in  the  case  of  completely  dissociated  solutions.  On  mix- 
ing solutions  of  sodium  chloride  and  potassium  nitrate,  for  example, 
some  undissociated  potassium  chloride  and  sodium  nitrate  must 
result,  whereby  the  relations  are  complicated.  « 

Solutions  which,  when  mixed,  do  not  mutually  affect  the  indi- 
vidual conductivities,  have  been  called  by  Bender  "corresponding 
solutions,"  and  by  Arrheiiius,  who  investigated  acid  solutions 
chiefly,  "isohydric  solutions."  Two  solutions  are  now  said  to  be 
isohydric  when  the  concentration  of  the  common  ion  is  the  same  in 
each  solution.  No  change  in  dissociation  occurs,  then,  upon  mixing 
them.  This  will  be  evident  from  the  following  discussion  :  — 

Consider,  for  example,  one  solution  to  be  of  acetic  acid  and  the 
other  of  salicylic  acid.  For  the  solution  of  acetic  acid,  according  to 
the  law  of  mass  action,  we  have  the  equation, 

Of   X    Ct    _       Ci 

-- 


and  for  salicylic  acid,  the  equation, 
^  t  X  C  j      C  i 

—   -- 


in  which  CHAc,  OHsai>  ^»  an(^  ^'<  represent  the  concentrations,  in  the 
respective  solutions,  of  the  undissociated  acetic  acid,  the  undisso- 
ciated salicylic  acid,  each  ion  in  the  acetic  acid  solution,  and  each 
ion  in  the  salicylic  acid  solution.  Since  the  solutions  are  isohydric, 
and  hence  are  of  equal  concentration  in  respect  to  hydrogen  ions, 


If  now  one  liter  of  the  acetic  acid  solution  be  mixed  with  four  liters 
i  Ztschr.  phys.  Chem.,  14,  673  (1894). 


CONDUCTANCE  OF  ELECTROLYTES  137 

of  the  salicylic  acid  solution,  the  contraction  in  volume  is  negligible 
for  such  dilute  solutions,  and  the  resulting  concentrations  of  the 
various  constituents  in  the  mixed  solution  are  as  follows  :  — 

Hydrogen  ions  =  Ct  or  Ot  (unchanged). 

Acetate  ions  (CH3COOf)  =  £  Ct. 

Undissociated  molecules  of  acetic  acid       =£  CHAC- 
Salicylate  ions  (C6H5OCOO')  =  f  C\. 

Undissociated  molecules  of  salicylic  acid  =  £  CUSal. 

By  substitution  of  these  new  values  in  the  above  equations  we  ob- 
tain, for  acetic  acid  in  the  mixture, 

c.c> 


or 


and  for  the  salicylic  acid  in  the  mixture, 


or  _.._ 

LHSal. 
'HSal 


Therefore  upon  mixing  the  two  solutions  no  change  in  dissociation 
should  take  place,  since  the  requirements  for  equilibrium  between  the 
ions  and  the  Undissociated  molecules  in  each  case  remain  satisfied. 
Finally,  it  is  evident  that  this  is  still  true  whatever  the  volume  of 
the  one  solution  may  be  which  is  mixed  with  a  given  volume  of  the 
other ;  and,  further,  that  when  two  solutions  are  isohydric  in  reference 
to  a  third  solution,  they  are  also  isohydric  in  reference  to  each  other. 
From  what  has  just  been  said,  it  may  be  concluded  that  solutions 
of  a  chloride,  or  of  a  bromide,  etc.,  of  the  same  metal,  or  of  nitrates 
of  closely  related  metals,  of  the  same  equivalent  concentration,  are 
nearly  isohydric,  since  they  are  dissociated  to  nearly  the  same  extent. 
Hence  the  conductivity  of  a  mixture  of  such  solutions  is  very  nearly 
equal  to  the  average  of  the  conductivities  of  the  individual  solutions. 
Upon  this  fact  may  be  based  a  method  of  quantitative  chemical 
analysis.  If,  for  example,  the  conductivities  of  two  solutions  of 
potassium  chloride  and  potassium  bromide  of  equal  percentage  con- 


138  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

centration  are  K  and  s',  respectively,  then  the  conductivity  of  a 
mixture  of  these  solutions  K"  is  given  by  the  equation  — 


when  m  and  1  —  m  represents  the  quantity  of  potassium  chloride  and 
of  potassium  bromide,  respectively,  contained  in  a  unit  quantity  of 
the  mixture.  When  the  value  of  K"  is  determined,  the  value  of  m 
is  easily  obtained  from  the  above  or  the  following  equation:  — 


K'-K 

Since  here  only  conductivity  ratios  are  involved,  it  is  evident  that 
the  conductivity  measurements  may  be  expressed  in  any  system  of 
units  without  changing  the  value  of  m.  It  is  most  convenient  to  ex- 
press these  values  in  terms  of  the  conductivity  of  a  simple  solution. 
The  inaccuracy  of  m  increases  with  the  differences  between  K  and  K'. 

In  general,  it  is  best  to  ascertain  whether  or  not  the  conductivities 
of  any  two  solutions  in  question  are  in  fact  additive  in  a  mixture  of 
them  by  means  of  measurements  carried  out  with  known  mixtures  ; 
for  two  other  factors  now  to  be  mentioned  may  exert  a  disturbing 
influence.  There  may  be  a  complex  compound  formed  when  the 
two  solutions  are  mixed,  in  which  case  the  equations  deduced  above 
no  longer  apply.  The  fact  that  the  conductivity  of  'the  mixture  is 
not  the  average  of  the  conductivities  of  the  constituent  solutions 
may  even  serve  to  detect  the  presence  of  such  complex  compounds. 
Secondly,  the  nature  of  the  solvent  may  be  changed  by  the  mixing 
of  the  two  solutions,  resulting  in  a  change  in  the  degree  of  dissocia- 
tion and  in  the  internal  friction  which  the  ions  must  overcome  dur- 
ing migration.  For  instance,  potassium  chloride  is  dissociated  to  a 
greater  extent  when  dissolved  in  pure  water  than  when  dissolved  in 
a  mixture  of  water  and  acetic  acid  containing  a  considerable  portion 
of  the  latter  liquid.  (See  later.)  For  the  same  reason,  the  addition 
of  considerable  quantities  of  acetic  acid  or  of  any  other  substance 
may  change  the  conductivity  of  an  electrolyte.1 

Finally  it  should  be  remembered  that,  as  a  matter  of  fact,  the 
requirements  of  the  law  of  mass  action  are  not  always  realized. 
The  following  empirical  rule,  which  is  of  wide  applicability  when 
no  complex  compounds  are  formed,  is  therefore  of  considerable 
value.  The  conductivity  and  the  freezing-point  lowering  of  a  mixture 
of  salts  having  one  ion  in  common  are  those  calculated  under  the  assump- 
tion that  the  degree  of  ionization  of  each  salt  is  that  which  it  would 

Ztschr.  phys.  Chem.,  40,  222  (1902). 


CONDUCTANCE   OF  ELECTROLYTES  139 

have  if  it  was  present  alone  at  such  an  equivalent  concentration  that 
the  concentration  of  either  of  its  ions  is  equal  to  the  sum  of  the  equiva- 
lent concentrations  of  all  of  the  positive  or  negative  ions  present  in  the 
mixture.1 

Assuming  that  a  mixed  solution  of  sodium  chloride  and  sodium 
sulfate  is  0.1  normal  in  respect  to  the  first  salt,  0.2  normal  in  respect 
to  the  second  salt,  and  0.18  normal  in  respect  to  the  common  positive 
ion  (or  to  the  negative  ions),  then  according  to  the  above  rule  the 
degree  of  dissociation  of  each  of  these  salts  in  the  mixture  is  the 
same  as  it  would  be  in  pure  water  when  its  ion  concentration  is  0.18 
normal. 

In  explaining  this  further,  it  is  recalled  that  the  following  equa- 
tion holds  for  a  single  salt  dissolved  in  water  (see  page  126)  :  — 


Applying  this  equation  to  each  of  the  salts  in  the  above  mixed 
solution,  we  have, 

l-xl  =  Kl(xlCl  +  x2C$>  and  1  -  x2  =  Kfad  +  x2C2)l- 

The  concentration  of  the  common  ion  of  the  mixed  solution, 
ajjOi+o^Oa,  is  here  the  concentration  of  the  positive  or  negative  ions 
of  each  individual  salt  in  the  simple  water  solution.  Since  K±  and 
Kz  may  be  known  from  conductivity  measurements  in  the  case  of 
the  individual  salts,  and  since  naturally  the  concentrations  of  the 
two  salts  Ci  and  <72  are  known,  the  values  xl  and  x2  may  be  found. 
This  may  best  be  accomplished  by  repeated  trials  until  a  satisfactory 
approximation  is  obtained.  The  equivalent  conductance  of  the 
mixture  is  then  given  by  the  equation, 


where  (C-JT)  and  (CZD)  represent  the  fractions  of  an  equivalent  of 
the  two  salts,  respectively,  which  are  present  in  a  volume  D  of  the 
mixture.  The  sum  of  the  two  values  is  equal  to  unity.  It  follows 
from  this  that  the  conductivity,  or  specific  conductance,  is  given  by 
the  equation, 

K  =* 


If  the  empirical  rule  stated  above  is  valid,  then  the  value  of  the 
conductivity  of  the  mixed  solution  calculated  from  the  above  equa- 
tion must  agree  with  the  experimentally  determined  values. 

It  should  be  added  that  conductivity  measurements  have   been 

1  A.  A.  Noyes,  Technology  Quarterly,  17,  301  (December,  1904). 


140  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

used  in  chemical  analysis  in  other  cases,  namely,  in  the  deter- 
mination of  the  solubility  of  salts  which  are  but  slightly  soluble  in 
water,  as  carried  out  by  Hollemann,1  Kohlrausch,  and  F.  Eose. 
The  solubilities  of  such  salts  can  be  determined  by  ordinary  chemical 
methods  only  with  great  difficulty. 

If  the  solution  is  so  dilute  that  the  electrolyte  may  be  considered 
to  be  completely  dissociated,  then 


and  £0, 

from  which  the  value  of  De,  the  volume  in  cubic  centimeters  of  the 
saturated  solution  in  which  one  equivalent  of  electrolyte  is  dissolved, 
may  be  calculated  :  — 


The  values  of  Rx  and  Kc,  the  actual  resistance  of  the  solution  in  the 
conductivity  cell  and  the  cell  constant,  are  found  by  direct  experi- 
ment, while  that  of  K^  is  often  obtained  by  calculation.  The  value 
of  De  being  known,  the  solubility  is  determined. 

The  following  results  have  been  obtained  in  this  way  :  — 


SALT 

TEMPERATURE 

CONCENTRATION  OF  SATURATED  SOLUTIONS 

Silver  bromide     ,    >    .  • 
Silver  iodide    .... 

21.1° 

20.8° 

0.57  x  10-  9  Ce,  or  0.107    mg.  per  liter 
0.0035  mg.  per  liter 

In  determining  the  solubility  of  many  salts,  as  for  example  of  the 
carbonates  of  the  alkali  earths,  hydrolysis  must  be  taken  into  con- 
sideration (see  page  126).  Since  the  hydrolysis  may  be  driven 
back  by  the  addition  of  OH  ions,  the  conductivity,  not  of  a  solution 
of  the  salt  in  pure  water,  but  rather  of  one  in  a  dilute  alkali  solu- 
tion, should  be  measured.  The  true  value  of  the  solubility  can  then 
be  calculated  from  the  increase  in  conductivity  of  the  alkali  solu- 
tion which  takes  place  when  the  salt  is  dissolved  in  it. 

Finally,  it  should  be  mentioned  that  Ktister 3  has  recently  shown 

1  Ztschr.  phys.  Chem.,  12,  125  (1893). 

2  Ztschr.  phys.   Chem.,  12,  234    (1893).      See  also  Sitzungsber.   d.   konigl. 
Pr.  Akademie  d.  Wiss.  Physik.  Mathem.  Kl.,  41,  1018  (1901)  ;    Ztschr.  phys. 
Chem.,  50,  355  (1905). 

8  Ztschr.  anorg.  Chem.,  35,  454  (1903);  42,  225  (1904).  This  application 
was  suggested  by  Kohlrausch  as  early  as  1885.  See  Wied.  Ann.,  26,  225  (1885). 


CONDUCTANCE  OF  ELECTROLYTES        141 

that  conductivity  measurements  may  often  with  advantage  replace 
indicators  in  the  titration  of  acids  and  bases.  If,  for  example,  10 
cubic  centimeters  of  a  0.1  normal  solution  of  HC1  be  diluted  to 
500  cubic  centimeters  and  titrated  with  a  0.1  normal  solution  of 
NaOH,  then  during  the  titration  the  rapidly  migrating  H  ions 
of  the  acid  are  gradually  replaced  by  the  slower  Na  ions,  and  con- 
sequently the  conductivity  of  the  acid  solution  gradually  decreases. 
After  all  H  ions  have  been  replaced  and  more  NaOH  is  added,  Na 
and  rapidly  migrating  OH  ions  are  increased  in  the  solution,  and, 
consequently,  the  conductivity  of  the  solution  being  titrated  is  also 
increased.  Hence  the  end  point  of  the  titration  is  the  point  at  which 
the  conductivity  reaches  its  minimum  value.  In  carrying  out  a 
titration  in  this  manner,  care  must  be  taken  to  insure  good  stirring 
and  constant  temperature. 

Regularity  of  lonization.  Reactivity  of  Electrolytes.  —  It  follows 
from  what  has  already  been  said  in  regard  to  electrical  con- 
ductivity that  different  substances  when  dissolved  in  water  or  in 
any  other  solvent  often  dissociate  to  very  different  degrees.  The 
question  at  once  arises  whether  the  ionization  of  different  substances 
follows  any  regular  scheme.  It  may  first  be  questioned  whether 
additive  relations  exist,  or,  in  other  words,  whether  for  a  given  atom 
or  atom-group  there  always  exists  the  same  tendency  or  force  tend- 
ing to  form  ions.  If  this  was  actually  the  case,  and  if  this  ten- 
dency always  appeared  in  the  same  way,  the  following  would  be 
observed:  G-iven  all  the  electrolytes  with  a  certain  negative  ion 
arranged  in  the  order  of  magnitude  of  their  dissociations,  then  this 
order  would  not  be  changed  if  another  negative  ion  was  substituted 
throughout  the  series.  From  a  study  of  experimentally  determined 
facts,  however,  it  is  seen  that  this  assumption  is  untenable.  Thus  it 
is  found  that  hydrochloric  acid  is  always  dissociated  to  a  greater 
extent  than  any  metal  chloride  in  a  solution  of  the  same  normality ; 
while  acetic  acid  is  always  less  dissociated  than  any  metal  acetate. 
Moreover,  zinc,  cadmium,  and  mercury  salts  are  notable  exceptions 
among  salts.  With  the  halogens  these  metals  form  electrolytes  which 
are  but  slightly  dissociated,  and  with  many  organic  anions  they  form 
electrolytes  which  are  largely  dissociated.  The  degree  of  dissocia- 
tion of  the  corresponding  acids  is  in  the  reverse  order.  Up  to  the 
present,  furthermore,  no  other  simple  relation  concerning  the  regu- 
larity of  ionization  has  been  discovered. 

It  may,  however,  be  stated  that  in  general  all  salts  dissolved  in  water 
are  highly  dissociated,  while  acids  and  bases  show  very  great  variations 
in  this  respect,  some  being  highly  and  some  but  slightly  dissociated. 


142  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

Solutions  of  substances  not  included  in  these  classes  generally 
possess  a  small,  yet  by  exact  measurements  detectable,  conductivity. 

If  a  chemical  process  is  capable  of  taking  place  between  two 
dissolved  substances,  it  always  takes  place  instantaneously  if  the 
substances  are  dissociated  to  a  moderate  degree.  The  usual 
reactions  of  analytical  chemistry  may  be  cited  as  examples.  In 
other  cases  in  which  the  substances  are  either  dissociated  to  an 
extremely  slight  degree,  or  to  a  degree  beyond  our  means  of  detec- 
tion, the  reactions  usually,  but  not  always,  take  place  slowly  at 
ordinary  temperatures.  Thus  in  the  preparation  of  organic  com- 
pounds, it  is  usually  necessary  to  carry  out  the  reactions  involved 
at  a  high  temperature  in  order  to  obtain  a  satisfactory  yield  with- 
out an  undue  expenditure  of  time.  Nevertheless,  it  should  not  be 
claimed  that  chemical  reactions  can  take  place  only  when  the  sub- 
stances involved  are  ionized.  Such  a  claim  is  decidedly  too  broad  and 
is  not  in  harmony  with  facts  ;  for  undissociated  substances  can  react 
with  each  other,  and  in  some  cases  with  a  high  velocity.  This  is  shown 
in  an  especially  striking  manner  by  the  investigation  of  Kahlen- 
berg,1  according  to  which,  solutions  of  stannic  chloride  and  of  cop- 
per oleate  in  benzene,  which  were  nonconductors  of  the  electric  cur- 
rent, when  mixed  immediately  gave  a  precipitate  of  copper  chloride 
with  the  simultaneous  formation  of  stannic  oleate. 

Solvents  other  than  Water.  Relation  between  the  Dissociating^ 
Power  and  the  Dielectric  Constant  of  Solvents.  —  Already  a  large 
number  of  investigations  have  been  carried  out  with  solvents  other 
than  water  or  with  mixtures  of  various  solvents.  It  would  be 
natural  to  expect  that  the  conceptions  which  have  been  found  ser- 
viceable in  the  case  of  solutions  in  water  could  be  applied  directly 
to  solutions  in  other  solvents,  keeping  in  mind  that,  according  to 
the  individual  nature  of  any  given  solvent,  the  degree  of  dissocia- 
tion, the  migration  velocity  of  the  ions,  and  consequently  the  con- 
ductivity of  a  solution  of  a  given  concentration  would  be  different. 
It  is  a  noteworthy  fact,  however,  that  the  behavior  of  non-aqueous 
is  much  more  complicated  than  that  of  aqueous  solutions.  This  is 
shown  especially  by  the  investigation  of  the  conductivity  of  solu- 
tions of  various  substances  in  liquid  sulfur  dioxide  made  by  "Walden 
and  Centnerszwer.2  Neither  the  law  of  the  independent  migration 
of  the  ions,  nor  the  law  that  by  increasing  dilution  the  conductance 
approaches  a  maximum  value,  nor,  finally,  the  dilution  law,  was 

1  J.  phys.  Chem.,  6,  9  (1902). 

2  Ztschr.  phys.  Chem.,  39,  513  (1902),  and  Walden,  Ztschr.  phys.  Chem.,  43, 
385  (1903). 


CONDUCTANCE  OF  ELECTROLYTES 


143 


found  to  hold.  Molecular  weight  determinations  carried  out  at 
the  same  time  by  the  boiling-point  method  gave  normal  values 
for  non-electrolytes,  and  abnormally  large  values  for  electrolytes, 
whereas  abnormally  small  values  would  be  expected.  This  indi- 
cates that  association  has  taken  place  to  a  considerable  extent, 
which  in  all  probability  takes  place  not  only  between  molecules  of 
dissolved  substance,  but  also  between  these  molecules  and  those  of 
the  solvent.  Considering  these  circumstances,  it  is  very  fortunate 
for  the  advance  of  the  sciences  of  chemistry  and  electro-chem- 
istry that  such  complications  are  generally,  although  not  always,1 
absent  in  the  case  of  aqueous  solutions.  It  is  due  to  this  fact  that 
it  has  been  possible  to  deduce  simple  laws  from  a  study  of  such 
solutions. 

Although  for  solvents  other  than  water  a  single  generalization 
under  which  individual  results  may  be  brought  is  still  lacking,  it 
is,  nevertheless,  important  to  consider  some  of  the  individual  results 
themselves.  A  summary  of  such  results  compiled  by  Walden2  is 
therefore  presented  here. 

The  solvents  which  have  been  most  frequently  investigated 
belong  to  the  alcohol  class  and  are  given  in  the  following  table :  — 


SOLVENT 

Methyl  alcohol, 
Ethyl  alcohol, 
Propyl  alcohol, 
Isopropyl  alcohol, 
Isobutyl  alcohol, 


FORMULA 
CH3OH 
C2H6OH 
C3H7OH 
C3H7OH 
C4H9OH 


SOLVENT 

Trimethyl  carbinol, 
Isoamyl  alcohol, 
Glycerine, 
Benzyl  alcohol, 


FORMULA 
(CH-OsCOH 
C6HnOH 
C3H6(OH)3 
C6H6CH2OH 


The  conductivity  of  solutions  of  a  large  number  of  salts  (includ- 
ing others  besides  those  of  the  alkalies),  acids,  and  bases  have  been 
determined.  In  the  case  of  methyl  and  of  ethyl  alcohol,  the  disso- 
ciation constant  of  many  salts  were  determined  both  by  the  boiling- 
point  and  by  the  conductivity  method,  without,  however,  obtaining 
anything  like  a  satisfactory  agreement.  According  to  the  results 
obtained  by  the  former  method,  the  molecular  weight  of  the  salts 
decreases  with  increasing  dilution.  It  was  not  possible,  however, 
to  obtain  a  dissociation  constant  independent  of  the  dilution,  either 
in  the  case  of  these  or  of  other  alcohol  solvents.  It  is  a  remarkable 
fact  that  only  in  the  case  of  solutions  of  trichloracetic  acid  has  the 
dilution  law  been  found  to  hold. 

1  W.  Biltz,  Ztschr.phys.  Chem.,  40,  185  (1902). 

2  Ztschr.  phys.  Chem.,  46,  103  (1903).    An  extensive  list  of  references  to  the 
literature  of  the  subject  is  also  given. 


144  A   TEXT-BOOK   OF  ELECTRO-CHEMISTRY 

Of  the  acids,  the  following  have  been  used  as  ionizing  substances  : 

Acetic  acid,  Butyric  acid, 

Formic  acid,  Benzoic  acid  (fused), 

Propionic  acid,  o-Nitrobenzoic  acid  (fused). 

With  the  solvent  formic  acid,  the  following  values  were  obtained 
at25°:  — 

K^  (for  KC1)  =  60.8 ;  K^  (for  NaCl)  ==  47.5. 

A  considerable  difference  was  found  between  the  dissociation  values 
obtained  by  the  freezing-point  method  and  those  obtained  by  the 
conductivity  method.  The  dilution  law  does  not  hold  for  these 
solutions. 

Some  of  the  nitriles  are  excellent  ionizers ;  namely,  the  following 
lower  members :  — 

Aceto-nitrile,  Butyro-nitrile, 

Propio-nitrile,  Benzo-nitrile. 

In  aceto-nitrile,  silver  nitrate  possesses  an  abnormally  small  molecu- 
lar weight  corresponding  to  electrolytic  dissociation ;  in  benzo-nitrile 
it  possesses  an  abnormally  large  molecular  weight,  indicating  the 
existence  of  polymerization. 

Of  the  ketone  solvents,  acetone  is  the  most  interesting.  The 
equivalent  conductance  of  binary  salts  dissolved  in  it  increases  con- 
siderably with  increasing  dilution,  without,  however,  attaining  a 
maximum  value.  In  this  case  also  the  dilution  law  does  not  hold. 

Of  the  other  groups  of  organic  compounds  which  have  been  in- 
vestigated, the  following  may  be  mentioned  :  — 

Aldehydes,  Nitrogen  bases  (pyridene), 

Esters,  Nitro-compounds, 

Ethers,  Hydro-carbons. 

It  has  already  been  shown  that  water  possesses  a  conductivity  of 
its  own.  Do  other  pure  solvents,  organic  and  inorganic,  also  con- 
duct the  electric  current  ?  It  has  been  found  that  the  conductivity 
of  most  of  the  good  ionizing  solvents  (S02C12,  S02,  NH3,  AsCl3),  be 
they  organic  or  inorganic,  is  of  the  same  order  of  magnitude  as  that 
of  water,  varying  between  the  limits, 

K^  =  1  •  10-7  to  5  •  10-7  • 

Nevertheless,  some  solvents  have  been  found  which  possess  high  con- 
ductivities, as  will  be  evident  from  the  following  table  :  — 


CONDUCTANCE   OF   ELECTROLYTES 


145 


SOLVENT 
Form-amide, 
Acet-amide, 
Acetyl  acetone, 
Formic  acid, 


CONDUCTIVITY 
4.7 -10-*    (25°) 
29-10-*   (81°) 
1.6. 10-*   (25°) 
1.5  •  10-*  (8.5°) 


SOLVENT  CONDUCTIVITY 

Nitric  acid  (anhydrous), 1525  •  10~*(0°) 
Sulfuric  acid  (anhydrous), 

1000. 10-*  (approx.)  (25°) 
Antimony  trichloride,  11.7  - 10-*(80°) 


These  conductivities  approach  those  of  typical  electrolytes. 

There  are  other  solvents  which  possess  no  conductivity  even 
when  salts  or  acids  are  dissolved  in  them.  Such  solvents  are  PBr3, 
SnCl*,  SbCl5,  SiCl4,  and  bromine. 

It  is  interesting  to  note  that  the  conductivity  of  pure  organic 
(also  of  liquid,  i.e.  fused,  inorganic)  substances  has  been  shown  to 
be  dependent  on  the  constitution  of  the  substance  in  question.  The 
first  member  of  homologous  series  possesses  the  highest  value, 
which  is  decreased  with  each  successive  introduction  of  a  CH^group. 
Substances  containing  OH-  or  CO-groups  give  the  highest  values  of  £. 

If  we  hold  to  the  dissociation  theory,  we  must  assume  that  all 
substances  which  conduct  electricity  electrolytically  are  ionized.  In 
regard  to  the  nature  of  this  ionization,  we  can  only  surmise. 

It  is  a  remarkable  fact,  finally,  that  iodine,  IBr,  IC1,  and  IC13, 
when  dissolved  in  S02C12  conduct  the  electric  current. 

According  to  Thomson  and  Nernst l  there  exists  a  relation  between 
the  dielectric  constant  and  the  dissociating  power  of  a  liquid.  In 
order  to  facilitate  the  understanding  of  this  relation  a  few  illustra- 
tions relating  to  the  dielectric  constant  K»  and  its  determination 
will  be  given.  .  ; 

Besides  the  galvanic  conductance,  there  is  also  a  second  constant 
by  which  the  electrical  behavior  of  a  body  is  characterized.  This 
constant  is  of  great  importance  in  the  case  of  just  those  substances 
which  conduct  electricity  galvanically  very  little  or  not  at  all,  i.e. 
the  so-called  insulators  or  dielectrics.  The  dielectric  constant,  KD, 
of  a  substance  is  proportional  to  the  capacity  of  a  condenser  the 
insolating  layer,  or  dielectrum,  of  which  is  this  substance.  If  the 
capacity  of  the  condenser  in  air  is  represented  by  k  (although  usually 
placed  equal  to  unity)  and  its  capacity  in  the  medium  in  question 
by  &!,  then  the  value  of  the  dielectric  constant  is  given  by  the 
equation, 


The  dielectric  constant  may  also  be  defined  as  the  factor  which 
gives   the   decrease   in    the    electrostatic   attraction   between    two 

1  Ztschr.phys.  Chem.,  13,  531  (1894). 


146  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

charged  spheres  when  the  latter,  while  maintained  at  a  constant 
distance  from  each  other,  are  transferred  from  a  space  filled  with 
air  to  one  filled  with  the  non-conducting  medium  being  investigated. 

A  method  for  the  determination  of  this  constant  which  is  very 
often  used  is  that  known  as  the  Nernst  Method.1  It  will  be  briefly 
considered. 

Starting  with  the  apparatus  used  in  the  Kohlrausch  method  for 
the  determination  of  electrical  conductivity  as  shown  in  Figure  29 
and  replacing  the  two  resistances,  the  known  and  the  unknown,  in 
the  Wheatstone  bridge  by  two  condensers,  an  apparatus  is  obtained 
with  which,  as  had  already  been  shown  by  Palaz,  the  capacities  of 
the  two  condensers  may  easily  be  obtained  in  case  the  dielectrics  are 
good  insulators.  The  minimum  sound  is  heard  in  the  telephone 
only  when  the  following  relation  obtains  (see  also  page  104)  :  — 


If  the  resistance  RI  is  made  equal  to  the  resistance  R2,  the  two 
condensers  placed  in  air  and  one  of  them  fcx  varied  in  a  known 
manner  until,  at  a  value  &/,  a  minimum  tone  is  heard  in  the  tele- 
phone, then  the  capacities  of  the  two  condensers  are  equal.  If  now 
the  dilelectrum  to  be  investigated  be  inserted  in  the  condenser  k2,  and 
the  condenser  fcj  be  again  varied  until  the  point  of  minimum  tone 
in  the  telephone  is  obtained  at  the  value  fc",  the  dielectric  constant 
of  the  substance  K»  is  given  by  the  equation, 


When  there  is  bad  insulation  in  the  condenser,  no  minimum  sound 
is  heard  in  the  telephone,  and  the  measurement  of  the  dielectric 
constant  cannot  be  carried  out  directly  by  the  above  method.  It 
can,  however,  be  determined  if  an  auxiliary  circuit  be  introduced, 
giving  the  other  condenser  a  suitable  conductance.  In  this  case, 
a  minimum  tone  is  heard  in  the  telephone  when  both  the  capacities 
and  the  conductances  of  the  two  condensers  are  equal.  By  means 
of  this  artifice,  it  is  at  once  evident  that  it  is  possible,  not  only  to 
determine  the  dielectric  constant  of  substances  which  conduct  gal- 
vanically,  but  also  to  determine  at  the  same  time  the  magnitude  of 
the  galvanic  conductance. 

The  principle  first  stated  by  Nernst,  expressing  the  relation 
between  the  dielectric  constant  and  the  dissociating  power  of  a 
solvent,  may  be  stated  as  follows  :  — 

i  Ztschr.  phys.  Chem.,  14,  626  (1894). 


CONDUCTANCE  OF  ELECTROLYTES        147 

The  greater  the  dielectric  capacity  of  a  solvent,  the  greater  is  the 
degree  of  electrolytic  dissociation  of  substances  dissolved  in  it,  when  the 
conditions  are  otherwise  the  same. 

The  following  consideration  will  make  this  principle  clearer: 
The  positively  and  negatively  charged  ions  would  unite  to  form 
electrically  neutral  molecules  because  of  the  electrostatic  attraction 
which  exists  between  them,  if  it  were  not  for  the  action  of  another 
and  opposing  force  the  nature  of  which  is  as  yet  unknown.  The 
equilibrium  between  these  two  forces  gives  rise  to  the  equilibrium 
between  the  ions  and  the  undissociated  molecules,  or  determines  the 
degree  of  dissociation.  When  the  dielectric  constant  is  increased, 
the  electrostatic  attraction  between  the  ions  is  alone  weakened,  and 
hence  the  degree  of  dissociation  is  increased. 

As  will  at  once  be  seen,  the  principle  stated  by  Nernst  is  well 
substantiated  by  the  very  recent  measurements  made  by  Walden.1 
Since  a  number  of  other  interesting  relations  are  furnished  by  these. 
results,  they  will  be  considered  somewhat  in  detail. 

Walden  determined  the  dissociating  power  of  half  a  hundred  sol- 
vents by  dissolving  in  them  one  and  the  same  binary  salt,  tetraethyl 
ammonium  iodide,  N(C2H6)4I,2  measuring  the  value  of  K  over  wide 
limits  of  dilution  and,  by  calculation,  extrapolating  for  the  value  of  K^. 
In  this  manner  he  was  able  to  calculate  for  the  different  solvents 
the  value  of  the  dissociation,  — 


. 

which,  for  equal  dilutions,  is  a  measure  of  the  dissociating  power. 
He  used  the  values  so  obtained  in  order  to  throw  light  on  the  in- 
fluence of  chemical  constitution  on  the  dissociating  power  of  various 
solvents,  and  found  that  the  dissociating  power  is  increased  by  the 
introduction  of  — 

a.  Oxygen-containing   radicals,  such  as  the  carboxyl,  hydroxyl, 
keto,  and  aldehyde  groups  ; 

b.  Nitrogen-  and  sulfur-containing  radicals,  such  as  the  cyanide, 
sulfocyanate,  isosulfocyanate,  nitro,  and  sulf  o  groups  ;  and 

c.  Oxygen  in  ring  compounds,  and  amido  groups  in  acid  amides. 
The  values  of  x  referred  to  a  volume  of  1000  liters  is  given  in  the 

following  table  in  the  order  of  the  relative  dissociating  power  for 
various  groups  combined  with  the  methyl  group. 

1  Ztschr.  phys.  Chem.,  64,  129  (1906). 

2  For  molecular  weight  determinations  for  this  salt  in  various  solvents  see 
Ztschr.  phys.  Chem.,  55,  281  (1906). 


148 


A   TEXT-BOOK  OF  ELECTRO-CHEMISTRY 


NAME 

FORMULA 

«  (%) 

Acetic  acid      ....... 

CH3-  COOH 

7 

Acetyl  chloride          .           • 

CH3  •  COC1 

72 

Acetone 

CH3  .  COCH3 

74 

Methyl  isosulf  ocyanate  .... 

CH3  •  NCN 
CH3  •  COH 

77 
84 

Methyl  alcohol      • 

CH3-OH 

88 

Methyl  sulfocyanate  

CH3  •  SCN 

89 

Methyl  cyanide    

CH3  •  CN 

90 

Nitro  methane      .                 ... 

CHs  •  NO2 

92 

A  study  of  the  homologous  series  of  organic  compounds  has 
shown  that,  as  the  carbon  content  increases,  the  dissociating  power 
decreases  with  greater  or  less  rapidity  in  much  the  same  way  as  in 
the  case  of  the  electrical  conductance  of  the  solvent. 

We  may  now  proceed  further  to  the  relation  between  the  dis- 
sociating power  and  other  physical  properties,  especially  that  of 
association.  According  to  the  assertions  of  some  investigators  a 
proportionality  should  exist  here,  and,  moreover,  the  value  of  KX 
should  depend  on  the  degree  of  association.  But  if  the  association 
factors  of  Ramsay  and  Shields  be  accepted,  then  it  follows  that  both 
of  these  assertions  are  untenable.  The  comparison  of  the  dis- 
sociating powers  of  various  solvents  with  their  dielectric  constants 
has,  however,  resulted  in  the  discovery  of  an  important  general- 
ization. It  has  been  found  that  a  direct  parallelism  exists  between 
the  dissociating  power  and  the  dielectric  constants  of  solvents,  com- 
pletely confirming  the  principle  put  forward  by  Nernst.  This  will 
be  at  once  evident  from  the  results  given  in  the  table  on  the  next  page. 

This  table  gives  an  interesting  survey  of  the  magnitude  of  K^  for 
the  various  solvents.  It  will  be  seen  that  it  varies  from  8  to  225, 
the  value  for  water,  112,  occupying  a  middle  position.  From  this 
fact  it  follows  that  it  is  inadmissible  to  draw  a  conclusion,  as  often 
has  been  done,  regarding  the  degree  of  dissociation  from  the  value  of 
the  equivalent  conductance  alone. 

It  is  remarkable  that  in  the  case  of  several  solvents  the  equivalent 
conductance  does  not  increase  with  increasing  dilution,  but,  according 
to  the  nature  of  the  solvent  and  of  the  electrolyte,  in  one  case  it  de- 
creases regularly,  while  in  another  it  varies  in  a  periodic  manner, 
passing  through  one  or  more  minima  and  maxima.  These  phe- 
nomena are  explained  on  the  assumption  of  chemical  interaction 
between  the  solvent  and  the  electrolyte. 

In  the  case  of  the  two  solvents,  acetonitrile  and  epichlorhydrine, 


CONDUCTANCE  OF  ELECTROLYTES 


149 


SOLVENT 

DIELECTRIC 
CONSTANT 

KD  (200) 

LIMITED 
VALUE  OF 
K«  («') 

DEGREE  OF 
DISSOCIATION 
D=     D=      D= 

100      1000      2000 

TBMPBRATURR 
COEFFICIENT 
±t  (0--26') 

Water  H2O 

81  7 

112 

(Per  cent) 
91      98       99 

1.  Formamide,  HCONH2  .... 
2.  Glycolnitrile,  H2COHCN   .  . 
3.  Ethylene  cyanide,  (CH2CN)2 
4.  Nitrosodimethylene      .... 
5.   Citracon  acidanhydride  .  .  . 
6.  Nitromethane,  CH3NO2  .  .  . 

84 
67.9 
57.3-61.2 
53.3 
39.5 
38.2-40.4 
36.5-394 

25 
71.5 
35.5(60°) 
95 
22.5 
120 
50 

93      98       98 
93      98       99 
90      95       96 
-    (89)      (91) 
82      93        94 
78      92        93 
78  1    91        93 

0.044 
0.0229-0.0219 
0.025 
0.0149-0.0144 
0.041  -0.044 
0.0132-0.0136 
0.0242-0.0254 

8.   Lactonitrile  

377 

40 

—      89        91 

0.0303-0.0328 

9.   Acetonitrile,  CH3CN    .... 
10.  Methyl  thiocyanate,  CH8SCN 
11.   Glycol,  (CH2OH)2  

35.8-36.4 
33.3-35.9 
34.5 

200 
96 
8 

74      90        92 

77      89        91 
78      89        — 

0.0103 
0.0148 
0.092  -0.096 

12.   Nitrobenzene,  C6H6NO2  .  .  . 
13.  Methyl  alcohol,  CH8OH  .  .  . 
14.  Cyauacetomethylester    .  .  . 
15.   Propiouitrile,  C2H5CN  .... 
16.   Ethyl  thiocyanate,  C2H6SCN 
17.  Cyanacetoethylester  
18.  Benzonitrile,  C6H5CN  .... 
19.   Epichlorhydrine  

33.4-37.4  1 
32.5-34.8  J 
28.8 
26.5-27.2  ' 
26.5-31.2 
26.2-26.7 
26.0 
(26  9) 

40 
124 
29.5 
165 
84.5 
28.2 
56.5 
66.8 

71      88        90 
73      88        90 
69      84        87 
65      84        87 
63      83        86 
65      83        87 
61      80        84 
60      81        85 

0.0254-0.0245 
0.0151-0.0159 
0.0439-0.0437 
0.0109-0.0112 
0.0149-0.0144 
0.0392 
0.0227-0.0231 
0.0168-0.0209 

20.   Ethyl  acetone    

25.1-26  0 

79 

—      83        87 

0.0172 

21.   Ethyl  alcohol  

21  7-27  4  } 

60 

54      78        82 

0.0230-0.0224 

22    Acetaldehyde     

28  6-21  1 

180(0°)  i 

—     (84       86) 

0.0082-0.0068 

23.  Acetone  
24.  Methyl  isothiocyanate  .... 
25.   Ethyl  isothiocyanate    .... 
26.   Propionaldehyde        

20.7-21.9. 
17.9-19.7 
19.4-22.0 
14.4-18.5 

225 

134(50°)i 
106 
(145  i 

50      74        80 
—      771      — 
—      66       — 
55      751)  1451 

0.0082-0.0090 
0.0101-0.011 
0.0124-0.0130 
(0.0081-0.011) 

27.  Acetic  acid  anhydride  .... 
28.   Benzaldehyde                   .  .  . 

17.9 
14  5-16  9  ^ 

76 
42.5 

58      79        84 
51      73        78 

0.0171-0.0177 
0.0207-0.0224 

29    Benzyl  cyanide 

15  0-16  7  I 

36 

46      74        79 

0.028  -0.031 

30.    Acetyl  bromide  

16.2          J 

114 

47      73        78 

0.0095 

31.   Anisaldehyde  
32.   Acetyl  chloride  

15.5 
155 

16.5 
1721 

—      76        81 

46      72        79 

0.063  -0.072 
0.007  -0.0088 

33.   Salicylaldehyde   

13  9  (19  2) 

25 

34      55        61 

0.0467 

34.   Isobutyric  acid  anhydride    . 
35.   Thioacetic  acid 

13.6 
12  8-17  3 

421 
771 

661      731 
—      681      741 

0.018 
0  0138 

36.  Benzoyl  acetic  acid  ester  .  . 
37.  Malonic  acid  dimethyl  ester 
38    Isovaleric  aldehyde 

11.0-14.3 
10.3 
10  1  11  8 

>7 

>25 

—      501      561 
—      —        41 

0.086  -0.097 
0.0285 
(0  0047-0  0123) 

39.  Acetic  acid  

646 

211 

—      (7)       (9) 

(0.057  -0.060) 

40.   Dimethyl  sulfide,  (CH8)2S    . 
41.   Ethyl  mercaptan,  C2H5SH    . 
42.   Aldoxime,  CH8CHNOH  .  .  . 
43    Tetranitromethane 

6.2 
7.95 
3.4 
<2  2 

44.   Dimethyl  sulfate  

465          i 

43 

—      91        93 

0.0230-0.0228 

45.   Diethyl  sulfate  

301 

43 

—      84        86 

0.024  -0  026 

46.  Asym.  Diethyl  sulfite, 
C2H6S08 
47.   Ethyl  nitrate 

38.6          J 
19  4-17  7 

26.4 
138  or  140 

—      94        95 
58(72)  67(78) 

0.0325-0.0327 
0  0105-0  0220 

48.  Sym.  Diethyl  sulfite, 
SO(OC2H5)2 
49.   Trimethyl  borate    

16.0 
8.0 

76 

188  i 

—      50       61 
—     (9")      (12) 

0.0111-0.0133 
0.0068 

1  Approximate. 


150  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

in  which  a  considerable  number  of  electrolytes  have  been  investi- 
gated, it  has  been  found  that  the  law  of  the  independent  migration 
of  ions  (Kohlrausch's  law)  is  valid. 

From  a  further  consideration  of  the  values  of  K^  given  in  the 
table  it  is  evident  that  there  also  exists  a  certain  relationship  be- 
tween them  and  the  chemical  constitution  of  the  solvent.  For 
example,  in  homologous  series  the  value  decreases  with  increasing 
carbon  content.  A  relationship  between  the  value  of  K^  and  the 
physical  properties  of  the  solvent  has  not  been  found.  On  the 
other  hand,  it  has  been  found  that  the  product  of  K^,  the  equiva- 
lent conductance  at  25°,  and  the  temperature  coefficient  for  the  con- 
ductance of  very  dilute  salt  solutions  varies  about  the  same  value  in 
the  case  of  solutions  differing  widely  from  each  other.  Otherwise 
expressed, 

K^  •  A,K(0°-25°)  =  1-30  (approx.), 

where  A,K(0°-25°)  =  —  -  £25°~£o°  • 

KQO  &D 

The  variation  from  the  value  1.30  is  considerable  only  in  the  case 
of  a  few  substances. 

There  is  also  a  numerical  relationship  between  the  dielectric  con- 
stants and  the  dilutions  in  various  solvents  which  give  the  same  de- 
gree of  dissociation.  The  relation, 

KD  VD  =K'»VD<=  J^VS"  -  =  Constant, 

where  KWK'WK"»  represent  the  dielectric  constants  of  the  individual 
solvents  and  D,  Z)',  D",  the  corresponding  dilutions  at  which  the  value 
of  the  degree  of  dissociation  is  the  same. 

From  the  table 1  on  the  next  page  it  may  be  seen,  further,  that  the 
dielectric  constant,  and  therefore  also  the  dissociating  power,  is  re- 
lated to  various  other  properties  of  the  solvent. 

As  the  value  of  the  dielectric  constant  K^  decreases,  it  is  seen 
that  the  values  of  the  latent  heat  of  vaporization  Hvap,  of  the  abso- 
lute conductance  of  heat  J£h,  and  of  the  critical  pressure  Pcrit,  also 
decrease,  while  the  values  of  the  van  der  Waal  constant  a  and  of  the 
molecular  volume  at  the  boiling  point  Vm  increase.  There  is  not, 
however,  a  strict  proportionality. 

At  this  point  it  should  be  mentioned  that  Euler2  has  noticed  that 
the  dielectric  constants  of  solutions  increase  with  their  ion  content. 
It  has,  for  instance,  been  shown  that  the  dielectric  constant  for 

1  Ztschr.  phys.  Chem.,  46,  172  (1903). 

2  Ibid.,  28,  619  (1899). 


CONDUCTANCE  OF   ELECTROLYTES 


151 


water  is  increased  by  the  addition  of  a  salt  to  it.  It  is  "possible 
that  this  fact,  even  if  not  alone,  plays  a  part  in  the  deviation  of 
strong  electrolytes  from  the  dilution  law  (see  page  125),  for  naturally 
the  law  can  only  hold  as  long  as  the  nature  of  the  solvent  remains 
unchanged. 


I 

II 

III 

IV 

v 

VI 

SOLVENT 

JTD 

Hvap. 

a 

rm 

pcnt. 

*k 

Water       

81  7 

536.5 

5.77 

18.9 

200 

0.154 

Methyl  alcohol       .... 
Ethyl  alcohol 

32.5 

21  7 

267.5 
205 

9.53 
15  22 

42.8 
623 

79 
62  8 

0.0495 
00423 

Propyl  alcohol  

12.3 

164 

16.32 

81.3 

50.2 

0.0373 

Formic  acid 

57  0 

103  7 

41  1 

00648 

Acetic  acid    

6.5 

89.8 

17.60 

63.8 

57.1 

0.0472 

Ammonia      

16 

329 

4.01 

29.2 

115 

Methyl  amine 

<10  5 

7  40 

72 

Ethyl  amine 

6  17 

9  44 

66 

i-Propyl  amine       .... 
Sulfur  dioxide  ^    .    .    .    . 

5.45 
14 

92  5 

13.7 
6  61 

85.6 

(normal) 

43  9 

50 
79 

— 

Acetone    

20  7 

125  3 

77  1 

60 

Methyl-ethyl  ketone  .     .    . 

Formic  methyl  ester  .     .     . 
Formic  ethyl  ester      ^  ...  •» 
Acetic  ethyl  ester       .     .     . 
Benzene                       .     .    . 

17.8 

8.87 
8.27 
5.85 
2  26 

116.1 
99.3 
86.7 
93  5 

11.96 

11.38 
15.68 
20.47 
18  36 

62.7 
84.7 
106.0 
96  2 

59.25 
46.83 
38.00 

47  9 

0.0378 
0.0348 
0  0333 

Toluene 

2  31 

83  6 

24  08 

118  3 

41  6 

0  0307 

Ether 

4  36 

84  5 

17  44 

106  4 

35  61 

0  0303 

Chloroform         

4  95 

58  5 

14.71 

84  5 

55  0 

00288 

Tetrachlormethane     .    .    .;.' 
Tin  tetrachloride    .    .    . 

2.18 
3.2 

46.35 
30.53 

19.20 
26.94 

103.7 
131.1 

45.0 
37.0 

0.0252 

The  Internal  Friction   and   Conductance  of  Organic  Solvents. — 

With  the  aid  of  his  comprehensive  series  of  measurements,  which 
have  already  been  mentioned,  and  also  of  new  determinations  of 
friction  coefficients  of  a  large  number  of  organic  solvents,  Walden1 
has  been  able  to  find  the  relation  which  exists  between  the  internal 
friction  of  a  dilute  solution  of  the  "normal  electrolyte"  N(C2H5)4I 
and  the  electrical  conductance  KW.  He  found,  moreover,  that  the 

1  Ztschr.  phys.  Cher*.,  55,  207  (1906). 


152  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

internal  friction  of  dilute  solutions  and  of  the  solvent  are  practically 
identical.  Hence  in  the  considerations  which  are  to  follow  this  one 
value  /  will  be  used. 

Walden  found  the  following  regularities :  — 

(a)  Both  the  internal  friction  and  the  conductance  are  dependent 
on  the  nature  of  the  solvent. 

(6)  The  smaller  the  friction,  the  greater  is  the  value  of  K^,  and 
conversely.  From  this  fact  the  relationship  between  the  internal 
friction  and  the  migration  velocity  of  the  ions,  N(C2H6)4'  and  I',  is 
evident. 

(c)  The  limiting  value  K230^  is  inversely  proportional  to  the  corre- 
sponding friction  coefficients  at  25°  t,  according  to  the  equation, 

Kr    .  vn    _  fii    .   ft 

£00  •    £    <*>  —  J      oo   •   J     oo> 

or,  in  general,  according  to  the  equation, 

B'.  •/'.  =  &"«•/".  =  Const. 

This  constant  varies  about  the  value  0.700,  between  the  limits  0.64 
and  0.71. 

With  the  use  of  one  and  the  same  electrolyte,  it  was  found  that  for  all 
of  the  thirty  solvents  which  were  investigated  the  product  of  the  internal 
friction  and  the  limiting  value  of  the  equivalent  conductance  was  the 
same,  although  the  individual  limiting  values  varied  from  about  8  to  225. 

With  the  aid  of  the  relation, 

f.-f~.='  0-700; 

it  is  possible  to  obtain  the  limiting  value  of  the  conductance  of  the 
"  normal  electrolyte  "  in  the  solvent  under  consideration  from  the 
value  of  the  internal  friction. 

Finally,  if  the  temperature  coefficients  of  friction  and  of  conduc- 
tance be  compared,  a  striking  agreement  is  found,  and  considering 
the  sources  of  error  involved,  it  may  be  said  with  great  probability 
that  for  one  and  the  same  solvent  the  two  coefficients  are  identical 

From  this  result  it  would  be  expected  that  the  above  relation 
between  friction  and  conductance  which  holds  at  25°  would  also 
hold  at  other  temperatures.  As  a  matter  of  fact  it  has  been  found 
that  at  0° 

K°;  ./°;  =  Const.  =  0.700. 

It  therefore  follows  that 

K*°  -fi=^-f:  =0.700. 

Hence  the  following  general  statement  may  be  made :  — 


CONDUCTANCE  OF   ELECTROLYTES  153 

With  the,  use  of  one  and  the  same  electrolyte  N(C2H5)4I  the  prod- 
uct of  the  internal  friction  and  the  limiting  value  of  the  equivalent 
conductance  is  independent  of  the  nature  of  the  solvent  and  of  the 
temperature  in  the  case  of  organic  solvents. 

'  In  order  to  explain  these  interesting  relations,  we  may  assume, 
as  did  Kohlrausch  in  the  case  of  aqueous  solutions,  that  the  migrat- 
ing ion  is  associated  with  a  large  number  of  molecules  of  the  solvent, 
and  consequently  in  its  forward  motion  encounters  a  friction  which 
is  identical  with  the  internal  friction  of  the  solvent.  It  is  then  clear 
that  the  temperature  coefficient  of  the  limiting  value  of  the  con- 
ductance and  that  of  the  internal  friction  must  become  identical. 

The  Electrical  Conductance  of  Salts  in  the  Fused  and  Solid 
States.  —  The  substances  which  conduct  the  electric  current  freely 
in  the  state  of  fusion  are  chiefly  salts  and  bases,  such  as  silver 
chloride  and  caustic  soda.  Their  conductance  can  be  determined  by 
the  method  used  by  Poincare,  by  using  silver  electrodes  and  adding 
a  trace  of  a  silver  salt  with  the  same  anion  as  that  of  the  salt  being 
investigated  in  order  to  avoid  polarization.  By  this  method  the 
measurement  can  be  carried  out  as  in  the  case  of  conductors  of 
the  first  class.  The  order  of  magnitude  of  the  equivalent  conduc- 
tance of  fused  salts  is  shown  by  the  values,  expressed  in  reciprocal 
ohms,  contained  in  the  following  table  :  — 


SALTS 

TEMPERATUBE 

EQITIV.  CONDUCTANCE 

KN08 

350° 

44.9 

NaNO8 

350° 

68.0 

AgN03 

350° 

60.9 

KC1 

760° 

90.6 

NaCl 

760° 

136.3 

In  order  to  compare  these  values  with  those  obtained  for  salts  in 
dilute  aqueous  solutions,  it  will  be  recalled  that  the  equivalent 
conductance  of  a  fiftieth  normal  solution  of  potassium  chloride  at 
18°  is  equal  to  119.96  reciprocal  ohms. 

The  results  thus  far  obtained  in  the  case  of  mixtures  of  fused 
salts  show  that  their  conductance  is  approximately  equal  to  the  sum 
of  the  conductances  of  the  constituent  salts. 

Not  only  above  the  melting  point,  but  also  below  it,  many  salts 
conduct  the  electric  current  readily.  Graetz  has  investigated  the 
conductance  of  salts  about  the  melting  point,  and  has  found  that  no 
considerable  sudden  change  in  the  conductance  occurs  as  the  melting 
point  is  passed.  On  the  other  hand,  the  temperature  coefficient  of 


154  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

the  conductance  reaches  a  maximum  value  in  the  vicinity  of  the 
melting  point. 

It  is  a  noteworthy  fact  that,  at  lower  temperatures  (10°  to  180°), 
according  to  the  investigation  of  Fritsch,1  the  addition  of  a  small 
quantity  of  a  salt  to  a  large  quantity  of  another  salt  is,  in  many  cases, 
accompanied  by  a  great  increase  in  the  conductance  of  the  latter  salt. 
This  is  a  striking  analogy  to  the  behavior  of  liquid  solutions,  justify- 
ing the  assumption  that  the  one  salt  exists  in  solid  solution  in  the  other. 

The  same  phenomenon  was  observed  by  Nernst2  in  the  case  of 
the  solid  oxides  such  as  magnesium  oxide,  and  it  is  upon  this  phe- 
nomenon that  the  Nernst  incandescent  lamp  is  based.  While  the 
conductance  of  the  pure  oxides  increases  but  slowly  with  the  tem- 
perature and  remains  comparatively  small,  that  of  a  mixture  of  the 
oxides  increases  rapidly,  attaining  finally  an  enormous  value.  For 
exaraple,  values  have  been  observed  which  were  about  six  times  as 
great  as  that  of  the  best  conducting  sulfuric  acid  solution  at  18°. 

The  fact  that  glasses  also  conduct  the  electric  current  electrolyti- 
cally,  or,  in  other  words,  through  the  migration  of  ions,  was  shown 
to  be  very  probable  by  the  pretty  experiment  made  by  Warburg  in 
the  year  1884.  He  used  a  piece  of  glass,  one  end  of  which  was 
dipped  in  sodium  amalgam  and  the  other  into  mercury,  as  the  elec- 
trolyte, through  which  he  passed  an  electric  current  from  the  amal- 
gam as  anode  to  the  mercury  as  cathode.  After  the  electricity 
had  passed  for  some  time  he  found  a  quantity  of  sodium  equiva- 
lent to  it  in  the  mercury.  Since  during  the  experiment  the  glass 
remained  clear  and  constant  in  weight,  it  must  be  concluded  that 
the  electricity  was  conducted  almost  entirely  by  means  of  sodium 
ions,  or,  in  other  words,  the  migration  velocity  of  the  anion,  perhaps 
Si03",  is  extremely  small.3 

Unipolar  Conduction.  —  It  was  already  observed  by  Ermann  about 
one  hundred  years  ago  that,  when  the  two  poles  of  a  galvanic  cell 
are  inserted  into  a  well-dried  piece  of  soap,  no  appreciable  continu- 
ous current  passes  through  the  circuit ;  and,  further,  that  when  one 
hand  is  brought  into  contact  with  the  positive  pole  and  the  moist- 
ened other  hand  is  pressed  upon  the  soap,  an  electric  shock  is 
received.  This  latter  phenomenon  is  not  observed  if,  instead  of 
the  positive,  the  negative  pole  is  touched  by  the  hand.  From  these 

1  Wied.  Ann,,  60,  300  (1897). 

2  Ztschr.  Elektrochem.,  6,  41  (1899) ;  see  also  E.  Bose,  Drude's  Ann.,  9,  164 
(1904). 

8  Further  particulars  regarding  the  conductivity  of  fused  salts  may  be  found 
in  the  book  of  Lorenz,  Die  Elektrolyse  geschmolzener  Salze,  1905,  W.  Knapp, 
Halle,  Saxony. 


CONDUCTANCE  OF  ELECTROLYTES  155 

facts,  as  well  as  from  electroscopic  experiments  which  have  been 
made,  it  is  to  be  concluded  that,  whereas  the  electric  current  may 
flow  unhindered  from  the  negative  electrode  into  the  soap,  it  cannot 
do  so  from  the  positive  pole,  but,  upon  attaching  an  auxiliary  circuit, 
such  as  that  from  hand  to  hand,  it  must  flow  exclusively  through 
this  circuit.  The  soap  was  called  by  Ermann  a  unipolar  conductor. 

The  phenomenon  of  unipolar  conduction  was  explained  by  Ohm 
by  assuming  that  electrolysis  takes  place  in  the  soap  the  moment  it 
is  connected  with  the  poles  of  the  cell,  by  which  alkali  is  separated 
at  the  negative,  and  the  fatty  acid  at  the  positive,  electrode.  The 
fatty  acid  is,  however,  a  nonconductor,  and  therefore  prevents  more 
or  less  completely  the  passage  of  electric  current  according  to  the 
water  content  of  the  soap. 

Similar  observations  may  be  made  in  the  case  of  the  electrolysis 
of  solutions  whenever  a  poor  conducting  substance  is  formed  at,  and 
adheres  to,  one  of  the  electrodes.  Very  recently  this  has  been  util- 
ized in  a  very  interesting  manner  in  transforming  an  alternating 
into  a  direct  current. 

If  aluminium  be  used  as  an  anode  in  a  solution  of  alkali  phosphate, 
or  of  alkali  salts  of  the  fatty  acids,  and  any  other  metal  as  a  cathode, 
a  poor  conducting  aluminium  compound  is  formed  on  the  surface  of 
the  aluminium,  which  prevents  the  passage  of  an  electric  current, 
even  when  a  potential-difference  of  200  volts  is  applied  at  the  elec- 
trodes. When  now  the  two  electrodes  are  connected  with  the  termi- 
nals of  a  circuit  carrying  an  alternating  current,  only  the  current  in 
one  direction  is  allowed  to  pass.  The  alternating  is  thus  trans- 
formed into  direct  current.  This  application  of  unipolar  conduction 
will,  however,  scarcely  become  of  practical  importance. 

It  appears  doubtful  that,  in  the  case  of  the  above  aluminium  cell, 
the  whole  action  can  be  explained  by  the  fact  that  a  relatively  thick 
layer  of  great  resistance  is  formed  at  the  anode.  It  is  more  probable 
that  a  thin  dielectrum  of  slight  conductance  is  formed  at  the  elec- 
trode, thus  forming  a  powerful  acting  condenser  in  the  circuit. 

Technical  Importance  of  Electrical  Conductivity.  —  A  knowledge 
of  the  conductivity  of  various  solutions  (and  of  fused  salts)  under  the 
most  varied  conditions  is  essential  to  the  rational  management  of  an 
electrolytic  industry,  for  it  should  always  be  the  aim  to  work  with 
the  best  possible  conducting  solutions.  Thus,  if  other  circumstances 
do  not  prevent  it,  a  solution  of  potassium  chloride  is  always  to  be 
preferred  to  a  solution  of  sodium  chloride  of  the  same  molar  con- 
centration. Furthermore,  it  is  always  preferable  to  carry  out  an 
electrolytic  process  at  a  high  temperature,  if  the  cost  of  heating 


156  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

does  not  exceed  the  saving  in  electrical  energy  due  to  the  increase 
in  conductivity.  Since  very  often  the  concentration  can  be  chosen 
at  will  inside  of  wide  limits  without  injury  to  the  process,  that  con- 
centration should,  in  such  cases,  be  chosen  which  has  the  greatest 
specific  conductance.  In  this  connection  it  should  be  remembered 
that,  in  the  case  of  electrolytes  which  are  very  soluble  in  water, 
the  specific  conductance,  or  conductivity,  in  contrast  with  the 
equivalent  conductance,  at  first  increases  and  then  decreases  with 
increasing  concentration.  This  is  shown  by  the  results  for  sulfuric 
acid  at  18°,  given  in  the  following  table :  — 


PERCENTAGE  CONCENTRATION 

SPECIFIC  CONDUCTANCE 

20 

0.6527 

25 

0.7171 

30 

0.7388 

35 

0.7243 

40 

0.6800 

70 

0.2157 

Hence,  whenever  sulfuric  acid  is  used  as  an  electrolyte,  as,  for 
example,  in  the  case  of  the  electrolytic  regeneration  of  chromic 
acid  where  only  about  100  grams  of  chromic  oxide  as  an  acid 
salt  in  sulfuric  acid  is  contained  in  one  liter  of  solution,  the  con- 
ductance is  increased  by  the  addition  of  an  electrolyte,  which  is 
without  injury  to  the  process.  In  the  above  chromic  acid  process 
sulfuric  acid  serves  as  such  an  electrolyte,  enough  being  added  to 
increase  the  specific  conductance  of  the  mixed  electrolytes  to  its 
maximum  value.  Very  often  it  is  necessary  for  the  electro-chemist 
to  make  his  own  measurements,  in  order  to  find  the  best  proportions 
of  electrolytes  to  use  in  a  given  case. 

The  investigation  of  the  cause  of  benzene  conflagrations1  has 
shown  that  the  practical  application  of  electrical  conductance  to 
poor  conductors  may  give  rise  to  great  fire  danger.  The  electro- 
static charges  generated  by  friction  are  prevented  from  being  con- 
ducted away  rapidly  enough  by  the  poor  conductance  of  the  pure 
benzene.  This  leads  to  the  formation  of  electric  sparks,  which,  of 
course,  may  easily  cause  explosions.  An  addition  to  the  benzene 
of  a  small  quantity  of  a  magnesium  salt  of  a  fatty  acid  increases 
the  conductance  sufficiently  to  prevent  the  formation  of  the  sparks. 

The  conflagrations  which  suddenly  break  out  during  work  with 
other  poor  conducting  organic  liquids,  such  as  acetone,  ether,  etc., 
may  be  explained  in  the  same  manner. 

1  Just,  Ztschr.  Elektrochem.,  10,  202  (1904). 


CHAPTER   VI 

ELECTRICAL     ENDOSMOSE.       MIGRATION     OF     SUSPENDED 
PARTICLES   AND   OF   COLLOIDS.     ELECTRO-STENOLYSIS 

As  early  as  the  year  1807  Reuss  observed  that,  during  the  elec- 
trolysis of  water  contained  in  a  vessel  which  was  divided  into  an 
anode  and  a  cathode  section  by  a  capillary,  or  a  system  of  capillaries 
such  as  a  porous  diaphragm,  the  water  was  carried  by  the  current  from 
the  former  to  the  latter  section.  In  the  case  of  the  better  conducting 
solutions,  this  phenomenon,  or  electrical  endosmose,  is  not  very 
pronounced. 

Later  on,  QuiDcke  and  G.  Wiedemann  carried  out  further  experi- 
ments in  this  direction.  The  following  statement  was  found  by 
Wiedemann  to  express  the  laws  of  electrical  endosmose  for  a  given 
liquid :  — 

The  quantity  of  a  given  liquid  carried  through  a  porous  diaphragm 
in  a  definite  time  varies  directly  with  the  current  strength  and  is 
independent  of  the  area  or  thickness  of  the  diaphragm. 

In  1809  Reuss  observed  that  suspended  particles,  such  as  clay, 
etc.,  are  migrated  under  the  influence  of  a  fall  in  potential.  When 
suspended  in  water,  they  are  migrated  toward  the  anode.  Recently 
such  migrations  in  the  case  of  the  so-called  colloidal  solutions  have 
been  closely  studied.  This  has  led  to  the  recognition  of  two  classes 
of  colloids,  namely,  positive  and  negative  colloids.  The  positive 
colloids,  such  as  gold,  platinum,  cadmium,  antimony,  arsenic  sulfide, 
molybdinum  blue,  indigo,  etc.,  migrate  toward  the  anode,  while  the 
negative  colloids,  such  as  ferric  hydroxide,  aluminium  hydroxide, 
chromium  hydroxide,  hemoglobin,  methyl  violet,  etc.,  migrate 
toward  the  cathode.  The  behavior  of  suspensions  of  nickel,  zinc, 
and  copper  oxide  is  more  complicated.  In  these  cases,  the  addition 
of  small  quantities  of  foreign  material,  such  as  traces  of  alkali  or 
of  acid,  changes  the  direction  of  migration. 

It  is  interesting  to  note  that  a  difference  between  positive  and 
negative  colloids  also  appears  in  the  case  of  their  precipitation.  The 
positive  colloids  are,  more  easily  precipitated  by  means  of  NaOH, 
while  the  negative  are  more  easily  precipitated  by  HC1.  The  former 

157 


158  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

are  also  precipitated  by  the  /3-radium  rays,  which  contain  negative 
electrons,  while  the  latter  are  not.  Finally,  if  the  two  kinds  of  col- 
loids are  brought  together,  they  precipitate  each  other.  It  is  a 
peculiar  fact,  however,  that  this  precipitation  does  not  take  place  if 
the  two  colloids  are  not  brought  together  in  certain  proportions.1 

It  is  evident  from  the  above  experiments  that  the  electric  current 
exerts  a  force  in  a  certain  direction,  not  only  upon  ions,  but  also  upon 
other  movable  bodies  of  matter.  This  may,  in  all  cases,  be  explained 
by  the  assumption  of  the  presence  of  an  electrical  charge  upon  the 
portion  of  matter,  in  question.  The  probability  that  this  assumption 
is  correct  is  greatly  increased  by  the  deductions  of  Helmholtz.  He 
reasoned  that  at  the  surfaces  of  contact  of  two  dissimilar  media,  for 
instance  the  contact  surface  of  water  and  glass,  an  electrical  charge 
or  double  layer  must  form.  The  existence  of  such  a  double  layer 
seems  comprehensible  from  the  results  of  experiments  on  the  for- 
mation of  contact  or  frictional  electricity.  If  now  a  potential-fall  is 
produced  in  a  liquid  by  the  passage  of  an  electric  current  through  it, 
then  the  positive  part  of  the  double  layer  is  attracted  by  the  negative, 
and  the  negative  part  by  the  positive,  pole.  Thereby  a  displacement 
of  the  two  layers  takes  place,  resulting,  when  the  force  of  the  current 
is  sufficiently  great,  in  the  migration  phenomenon  noted  above.  The 
movable  liquid  layer,  according  as  it  is  charged  positively  or  nega- 
tively, migrates  toward  the  cathode  or  anode,  respectively,  and  by 
means  of  friction  carries  with  it  the  neighboring  liquid  or  in  case 
the  migration  takes  place  in  capillaries,  the  entire  liquid.  The  dis- 
rupted double-layer  gradually  becomes  neutral  by  conduction,  form- 
ing a  new  double-layer,  and  the  process  goes  on  again.  By  means  of 
a  suitable  pressure,  moreover,  as  much  liquid  may  be  forced  back 
through  the  center  of  the  tube  as  is  brought  up  by  the  electric  cur- 
rent along  the  walls  of  the  tube,  thus  establishing  a  stationary  state. 
Conversely,  if  by  means  of  a  powerful  pressure  the  liquid  be  forced 
through  a  capillary  tube  so  that  the  charged  liquid  forming  a  part 
of  the  double  layer  is  forced  along  the  wall  of  the  tube  together  with 
the  current  of  liquid  in  the  middle  of  the  tube,  an  electric  current 
is  produced.  The  arrangement  is  entirely  analogous  to  the  ordinary 
electric  machine,  with  only  this  difference,  that  whereas  in  the 
former  case  a  liquid  rubs  past  a  solid,  in  the  electric  machine  a  solid 
rubs  past  a  solid. 

This  explanation  is  naturally  directly  applicable  to  the  migration 
of  suspended  particles.  These  particles  take  the  place  of  the  glass 
wall  and,  being  movable,  migrate,  in  the  opposite  direction  from  the 
1  Biltz,  Ber.,  37,  1095  (1904). 


ELECTRICAL  ENDOSMOSE  159 

water,  to  the  anode.1  The  question  arises  as  to  what  other  properties 
may  be  connected  with  this  phenomenon.  If  now  another  liquid 
be  substituted  for  water,  a  change  will  be  observed.  When  turpen- 
tine, for  example,  is  substituted,  it  migrates  to  the  anode,  while  the 
suspended  particles  migrate  to  the  cathode.  Coehn  gives  the  fol- 
lowing answer  to  the  above  question,2  which  he  has  confirmed  by 
many  experiments :  If  two  substances  are  brought  into  contact  with 
each  other,  that  one  possessing  the  higher  dielectric  constant  will  become 
positively  charged.  It  has  already  been  stated  that  water  possesses  a 
very  high  dielectric  constant.  This  fact  then  furnishes  a  ready 
explanation  for  the  migration  of  water,  in  most  cases,  to  the  cathode. 

The  technical  application  of  the  phenomenon  of  electrical  endos- 
mose  has  recently  been  undertaken.3  If  a  vessel,  the  opposite  sides 
of  which  are  formed  of  perforated  pieces  of  metal  serving  as  elec- 
trodes, be  filled  with  a  quantity  of  wet  turf,  and  an  electric  current 
be  passed  through  it,  water  bubbles  out  of  the  perforations  in  the 
side  forming  the  cathode.  This  is  a  striking  lecture  experiment.  The 
turf  itself  which  becomes  dried  acts  as  a  diaphragm,  while  the  water  is 
carried  to  the  cathode,  where  it  flows  off.  In  a  similar  manner  it  was 
endeavored  to  extract  the  sap  from  sugar  beets,  and  to  accumulate  it 
about  the  cathode,  preparatory  to  the  crystallization  of  the  sugar. 
It  is  not  at  present  known,  however,  whether  or  not  the  extensive 
experiments  have  shown  the  process  to  be  of  commercial  value. 

In  the  electrical  tanning  process,  electrical  endosmose  appears 
also  to  play  a  leading  role,  by  forcing  the  tanning  liquids  quickly 
into  the  pores  of  the  hides. 

An  observation  of  Braun  is  closely  related  to  electrical  endosmose. 
He  observed  that  when  a  salt  solution  separated  into  two  portions 
by  capillaries  is  electrolyzed,  a  deposition  of  metal  takes  place  in 
the  capillaries.  This  phenomenon  is  called  electrostenolysis.  Capil- 
laries, most  suitable  for  demonstration  purposes,  may  be  prepared  by 
dipping  the  hot  closed  end  of  a  glass  tube  into  cold  water.  This 
end  is  then  pierced  by  numberless  fine  cracks.  If  now  a  solution 
and  one  electrode  be  placed  in  this  tube,  and  the  tube  be  placed  in  a 
beaker  also  containing  solution  and  the  other  electrode,  the  desired 
apparatus  is  obtained. 

Electro-stenolysis  has   also  been   explained  by  Coehn.4     It  has 

1  Another  theory  has  been  advanced  by  Billitzer,  Ztschr.  phys.  Chem.,  45, 
307  (1905). 

2  Wied.  Ann.,  64,  217  (1898). 

8  German  Patents  124509,  124510,  128085. 

4  Ztschr.  Elektrochern.,  4,  501  (1898)  ;  Ztschr.  phys.  Chem.,  25,  651  (1898). 


160  A   TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

already  been  noted  that  with  a  sufficiently  great  potential-fall,  a 
displacement  of  the  positive  water  layer  takes  place,  leaving  the 
glass  wall  of  the  capillary  negatively  charged.  If  now  positively 
charged  metal  ions  are  present  in  solution,  they  will  be  attracted  to 
the  wall  of  the  capillary,  and  there  discharged  and  deposited.  To 
be  sure,  this  deposition  will  be  very  slight  since  very  large  electrical 
charges  are  present  on  the  ions.  The  metal  layer  deposited  cannot 
in  general  be  increased  by  taking  part  in  the  conduction,  because 
one  end  then  becomes  an  anode  and  loses  as  much  metal  as  the 
other  end  gains  as  cathode.  Under  these  circumstances,  only  a  dis- 
placement of  the  layer  in  the  direction  of  the  cathode  can  take  place. 
In  those  cases,  however,  in  which  the  weight  of  the  layer  can  in- 
crease by  taking  part  in  the  conduction  of  electricity,  the  trace  of 
deposited  metal  increases  and  finally  becomes  visible. 
Such  cases  are  the  following :  — 

1.  When  the  deposited  metal  is  not  oxidized  at  the  anode,  as,  for 
example,  the  platinum  salts. 

2.  When  an  insoluble  compound  is  formed  at  the  anode,  especially 
the  peroxides. 

3.  When,  in  the  case  of  salts  in  the  lower  state  of  oxidation,  the 
negative  ion  can  react  on  the   solution  with  the   formation  of  a 
higher  oxidized  salt  as  in  the  case  of  a  cuprous  chloride  solution. 
In  this  case  the  chlorine  liberated  oxidizes  the  salt  to  cupric  chloride. 

As  a  specially  interesting  result  of  the  experiments  substantiating 
these  statements,  it  may  be  mentioned  that  solutions  of  cobalt  salts, 
which  are  weakly  acid  through  hydrolysis,  show  stenolysis  regularly, 
while  in  the  case  of  nickel  salts  no  deposition  of  metal  is  visible. 
It  was  concluded  from  this  fact,  that  of  the  two,  only  the  cobalt 
salts  form  peroxides  by  electrolysis.  Utilizing  this  fact,  not  only 
a  simple  and  certain  qualitative  test  for  cobalt  in  nickel  solutions, 
but  also  a  quantitative,  although  somewhat  tedious,  separation  of 
the  two  metals  is  possible.1 

*  Ztschr.  anorg.  Chem.,  33,  9  (1903). 


CHAPTER  VII 

ELECTROMOTIVE  FORCE 

HAVING  dealt  in  the  previous  chapters  especially  with  the  one 
factor  of  electrical  energy,  the  quantity  of  electricity,  the  other 
factor,  the  electromotive  force,  will  now  be  considered. 

The  Determination  of  Electromotive  Force.  —  As  already  indicated 
in  the  introduction,  the  electromotive  force  of  a  cell  may  be  deter- 
mined by  means  of  a  delicate  galvanometer  through  an  application 
of  Ohm's  law, 


when  R^  is  made  so  great  that  BM  is  inconsiderable  in  comparison 
with  it.  In  this  case,  the  deflections  of  the  needle  of  the  galvanom- 
eter caused  by  two  different  cells  successively  introduced  into  the 
same  circuit  are  to  each  other  as  the  respective  electromotive  forces 
of  the  cells.  If  one  of  the  two  cells  be  a  normal  cell,  the  electro- 
motive force  of  the  other  cell  is  thus  easily  obtained  directly  in  volts 
If  the  internal  resistance  has  not  been  made  negligible  compared 
with  the  external,  the  electromotive  force  may  still  be  determined 
by  reading  the  galvanometer  deflections  caused  by  the  two  cells, 
both  connected  in  the  same  circuit,  first  in  series  and  secondly  in 
opposition  to  each  other.  In  this  case  we  have  the  equation, 


C2        F.—  F 

F= 


in  which  Cj  and  C2  are  the  currents  found  in  the  two  cases  ana 
•ffx  and  Fn  are  the  electromotive  forces,  respectively,  of  the  unknown 
and  of  the  normal  cell. 

In  more  general  use  than  the  above  method  is  that  devised  bj 
Poggendorf  and  known  as  the  compensation  method.    By  this  method, 
the  unknown  electromotive  force  is  exactly  compensated  by  a  known 
M  161 


162  A  TEXT-BOOK   OF  ELECTRO-CHEMISTRY 

electromotive  force.     A  diagram  of  a  convenient  form  of  apparatus 
for  this  method  is  shown  in  Figure  33.1 


Normal  Cell 

FIG.  33 

In  the  above  figure,  the  line  AC  represents  the  meter  wire  of  a 
Wheatstone  bridge  or  of  a  drum,  usually  of  about  ten  ohms  resist- 
ance. The  other  parts  are  named  in  the  figure.  When  the  storage 
cell  is  in  place,  a  current  flows  through  the  wire  AC  and  there  is  a 
definite  and  uniform  fall  in  potential  between  the  points  A  and  (7. 
In  order  to  obtain  the  value  of  this  potential-fall,  a  carefully  tested 
normal  cell  and  an  electrometer,  galvanometer,  or  any  other  instru- 
ment which  shows  when  no  current  is  flowing  in  a  circuit  are  con- 
nected in  an  auxiliary  circuit  as  shown  in  the  diagram,  and  the 
sliding  contact  B  is  moved  until  the  electrometer  indicates  that  no 
current  is  flowing  in  this  circuit.  The  potential-fall  between  the 
points  A  and  B  is,  then,  equal  to  the  known  electromotive  force  of 
the  normal  cell.  Since  the  fall  in  potential  is  uniform  along  the 
wire,  the  fall  per  millimeter  of  the  wire  may  then  be  calculated. 

The  unknown  electromotive  force  of  any  other  cell  may  now  be 
determined  by  substituting  it  for  the  normal  cell  and  again  moving 
the  sliding  contact  until  no  current  flows  in  the  circuit.  If  the  new 
position  of  the  sliding  contact  is  B',  then  the  unknown  electro- 
motive force  is  equal  to  the  known  potential-fall  from  the  point  A 
to  the  point  B'. 

When  the  electromotive  force  of  a  cell  is  to  be  measured,  that 
which  it  possesses  on  an  open  circuit  is,  in  general,  the  value 
desired,  for  the  value  which  would  be  obtained  while  the  cell  is  in 
action  would  be  indefinite  because  of  the  change  in  the  state  of  the 
electrodes  or  of  the  electrolyte  which  takes  place.  In  the  case  of 
electrometric,  and  especially  in  the  case  of  galvanometric,  meas- 
urements, the  conditions  under  which  no  current  flows  in  the 

1  For  a  more  detailed  description,  see  Ostwald-Luther,  Physiko-chemische  Mes- 
sungen,  page  367.  For  a  more  sensitive  potentiometer  based  on  the  same  prin- 
ciples, see  Jager,  Die  Normalelemente  (Wihl.  Knapp,  Halle,  Saxony,  1902). 


ELECTROMOTIVE  FORCE  163 

circuit  do  not  strictly  prevail  even  when  according  to  the  electrom- 
eter, or  other  instrument,  they  should  be  fulfilled.  This  is  due 
to  the  fact  that  every  instrument  consumes,  at  the  expense  of 
the  source  being  measured,  a  certain  quantity  of  electricity  for 
its  operation.  It  is  necessary,  therefore,  to  ascertain  whether  or 
not  this  quantity  of  electricity  is  greater  than  allowable,  or  in  other 
words,  whether  or  not  the  state  of  equilibrium  actually  measured  is 
appreciably  different  from  that  which  it  is  desired  to  measure.  As 
a  matter  of  fact,  in  the  case  of  measurements  made  on  gas  and 
similar  cells,  a  considerable  error  is  frequently  introduced  because^ 
of  failure  to  pay  sufficient  attention  to  the  sensitiveness  of  the 
galvanometer  or  to  the  capacity  of  the  electrometer. 

The  following  normal  cells  are  those  most  generally  used : l  — 

1.  The  so-called  Helmholtz  calomel  cell,  which  consists  of 

Zn  -  ZnCl2  solution  (sp.  gr.  1.409  at  15°)  -  HgCl  -  Hg. 

This  cell,  when  made  in  the  prescribed  manner,  possesses  an  electro- 
motive force  of  one  volt  at  about  15°  t.  The  change  of  the  electro- 
motive force  is  very  small,  being  equal  to  +  0.00007  for  a  rise  of  one 
degree. 

2.  The  Clark  cell,  which  consists  of 

Zn  -  ZnS04  paste  -  Hg2SO4  paste  -  Hg. 

When  made  according  to  the  specifications  of  the  "  Physikalisch- 
Technischen  Reichsanstalt,"  it  has  an  electromotive  force  of 

1.4328  -  0.00119  (t  -  15)  -  0.00007  (t  - 15)2  volts, 

where  t  is  its  temperature. 

(3)   The  Weston  or  cadmium  cell,  which  consists  of 

Cd  (better  a  10  to  15  %  amalgam)  -  CdS04  paste  -  Hg2S04  paste  -  Hg. 

This  cell,  when  made  in  the  prescribed  manner,  has  an  electro- 
motive force  of 

1.0186  -  0.000038  (t  -  20)  volts, 

and  is  preferable  to  the  Clark  cell,  because  its  temperature  coefficient 
is  nearly  zero. 

Eor  exact  measurements  it  is  recommended  that  normal  cells  be 
obtained  from  the  "Technischen  Reichsanstalt."  The  electro- 

1  For  further  particulars,  see  Ostwald-Luther,  Physiko-chemiscfte  Messungen, 
page  361  ;  Jager,  Ztschr.  Elektrochem. ,  8,  485  ;  and  Jager,  Die  Normalelemente 
(Wihl.  Knapp,  Halle,  Saxony,  1902);  Hulett,  Ztschr.  phys.  Chem.,  49,  483 
(1904). 


164  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

motive  force  of  these  cells  is  obtained  from  measurements  of  resist- 
ance and  current. 

Reversible  and  Irreversible  Cells.  —  Any  arrangement  which,  as  a 
result  of  a  chemical  reaction  or  of  such  physical  processes  as  diffu- 
sion, etc.,  is  capable  of  producing  electrical  energy  is  called  a  gal- 
vanic cell ;  whether  the  reaction  takes  place  between  a  liquid  and  a 
solid  or  between  two  liquids  does  not  come  into  consideration.  All 
cells,  or,  as  they  are  also  called,  elements,  may  be  divided  into  two 
classes,  namely,  into  those  which  are  reversible  and  those  which  are 
irreversible.  To  the  first  class,  for  example,  belongs  the  Daniell  cell, 
which  consists  of 

Zn  —  ZnS04  solution  —  CuSO4  solution  —  Cu. 

The  meaning  of  the  term  reversible  cell  may  be  made  clearer  by 
the  following  consideration :  Let  us  consider,  for  example,  a  Daniell 
cell,  the  electromotive  force  of  which  is  exactly  compensated  by 
another,  oppositely  directed,  electromotive  force.  If  the  latter  be 
now  slightly  diminished,  the  cell  at  once  becomes  active,  zinc  goes 
into  solution,  and  copper  separates  out.  On  the  other  hand,  if  the 
compensating  electromotive  force  be,  instead,  slightly  increased, 
thus  becoming  slightly  greater  than  that  of  the  Daniell  cell,  copper 
dissolves,  and  the  zinc  deposits  out  of  solution.  Hence,  if  the  con- 
dition of  the  cell  is  changed  by  a  process  like  the  former,  this 
change  may  be  exactly  compensated  and  the  original  condition  of 
the  cell  restored  by  a  process  like  the  latter,  i.e.  the  cell  is  reversible. 
Of  a  reversible  cell  it  is  theoretically  true  that  the  maximum  elec- 
trical energy  which  can  be  obtained  through  its  action  at  constant 
temperature  exactly  suffices  to  bring  it  back  to  its  former  condition. 
This  statement  may  also  be  taken  as  a  definition  of  a  reversible  cell. 

As  an  example  of  an  irreversible  cell,  that  one  discovered  by 
Volta  which  consists  of 

Zinc  —  dilute  sulf uric  acid  —  silver 

may  be  given.  When  this  cell  is  in  operation,  zinc  dissolves,  and 
hydrogen  separates  at  the  silver  electrode  and  is  lost.  From  this 
fact  alone  it  is  evident  that  the  original  condition  cannot  be  restored 
by  simply  reversing  the  current.  On  the  contrary,  in  this  case 
silver  goes  into  the  solution,  and  hydrogen  separates  at  the  zinc 
electrode. 

It  is  characteristic  of  reversible  cells  that,  when  the  current  is  not 
too  great,  the  electromotive  force  which  they  possess  immediately 
after  being  set  into  operation  remains  nearly  constant  as  long  as 


ELECTROMOTIVE   FORCE  165 

the  material  necessary  for  the  chemical  reaction  is  present.  On  the 
other  hand,  the  initial  high  electromotive  force  of  an  irreversible 
cell  falls  considerably,  and  reaches  a  nearly  constant  minimum  only 
after  some  time.  Hence  the  terms,  non-polar izable  and  polarizable, 
which  are  often  applied  to  these  two  classes  of  cells.  More  definite 
information  relating  to  these  phenomena  will  be  given  later,  in  the 
chapter  on  polarization.  It  may,  however,  be  stated  here  that  a 
metal  which  is  not  too  positive,  dipping  into  a  solution  which  contains 
a  sufficient  number  of  its  own  ions  (preferably  a  saturated  solution 
in  contact  with  some  of  the  solid  salt),  forms,  for  ordinary  current 
densities,1  a  non-polarizable  electrode.  In  the  case  of  the  Daniell 
cell  both  electrodes,  and  consequently  the  whole  cell,  is  non- 
polarizable. 

Since  at  the  present  state  of  science  the  actions  which  take  place 
in  reversible  cells  may  easily  be  comprehended,  and  even  quantita- 
tively followed,  they  may  now  be  considered  to  advantage.  , 

Relation  between  Chemical  and  Electrical  Energy  II.  —  The  ques- 
tion now  arises :  How  may  the  quantity  of  electrical  energy  which 
a  cell  is  capable  of  producing  be  calculated  from  the  chemical 
energy  expended,  —  or,  more  strictly  speaking,  —  from  the  heat 
effects  of  the  reactions  taking  place  in  the  cell,  since  the  latter 
still  constitute  our  measure  of  the  chemical  energy?  It  has  already 
been  mentioned  in  the  introduction  that  the  assumption  originally 
made  by  Helniholtz  and  William  Thomson,  that  the  quantities  of 
heat  involved  are  completely  transformed  into  electrical  energy,  is 
untenable.  It  is  only  in  certain  rare  cases  that  this  simple  relation 
exists.  About  thirty  years  ago  Gibbs,  Braun,  and  Helmholtz  suc- 
ceeded, by  calculation,  in  fixing  the  real  relations. 

The  first  law  of  energetics  may  be  stated  as  follows :  — 

Energy  can  neither  be  created  nor  destroyed,  and  consequently  the 
total  quantity  of  energy  is  a  constant. 

This  law  says  nothing  about  the  possibility  of  transforming  one 
energy  form  into  another,  and,  indeed,  from  it  alone  it  appears  as 
if  it  would  be  possible  to  transform  heat  at  constant  temperature 
into  work.  If  this  were  true,  it  would  no  longer  be  necessary  to 
use  expensive  coal  to  furnish  power  to  run  our  railroad  trains,  for 
the  inexhaustible  heat  energy  of  the  surroundings  could  be  used 

1  Current  density  may  be  defined  to  be  the  current  per  square  centimeter  of 
electrode  surface.  While  the  total  current  is  the  same  at  both  anode  and 
cathode,  the  current  density  at  the  two  electrodes  varies  according  to  the 
respective  sizes  of  the  electrodes.  It  is  therefore  usual  to  distinguish  an  anode 
and  a  cathode  current  density. 


166  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

instead.  As  a  matter  of  fact,  it  has  not  been  found  possible  to 
obtain  such  a  form  of  perpetual  motion,  called  perpetual  motion  of 
the  second  kind.  This  experience  has  resulted  in  the  formulation 
of  the  second  law  of  energetics,  which  excludes  the  unlimited  trans- 
formability  of  the  forms  of  energy.  It  was  expressed  by  Clausius 
as  follows :  — 

Heat  cannot  pass  of  itself  from  a  lower  to  a  higher  temperature. 

The  following  more  general  statement  of  the  law  by  Nernst  is, 
however,  to  be  preferred :  — 

"  Every  process  which  takes  place  of  itself  in  any  system,  or,  in  other 
words,  without  receiving  energy  in  any  form  from  the  surroundings,  is 
capable  of  furnishing  a  definite  quantity  of  work" 

Conversely,  such  a  process  can  be  made  to  take  place  in  the 
opposite  direction  only  by  the  expenditure  of  work  upon  it.  If  no 
spontaneous  processes  existed,  then  no  work  of  any  kind  could  be 
performed.  For  example,  at  constant  temperature,  and  excluding 
other  changes  in  state,  a  transformation  of  heat  into  work  is  im- 
possible. 

It  should  be  borne  in  mind  that  these  two  laws  of  energetics  express 
the  conclusions  of  experience  and  not  the  deductions  from  theories. 

The  maximum  external  work  which  a  spontaneous  process  is 
capable  of  furnishing  is  of  great  interest,  since  this  work  is  an  im- 
portant characteristic  of  the  process.  It  is  not  worth  the  trouble  to 
investigate  values  other  than  the  maximum  value,  because  they  are 
indefinite  and  may  vary  even  to  zero. 

From  a  closer  consideration,  it  is  evident  that  the  maximum 
quantity  of  work  is  obtained  from  a  process  when  it  is  made  to 
take  place  reversibly,  or,  in  other  words,  in  such  a  manner  that, 
theoretically  speaking,  at  every  instant  equilibrium  exists  in  the 
process. 

A  process  may  be  carried  out  isothermally  and  reversibly  in 
several  ways.  The  question  then  arises  as  to  whether  the  values  of 
the  maximum  work  obtained  in  these  different  ways  are  identical  ? 
Now  they  must  be  identical,  for  otherwise  perpetual  motion  of  the 
second  kind  would  result,  and  this,  according  to  the  second  law  of 
energetics,  is  an  impossibility.  Therefore  if  the  value  of  the  maxi- 
mum work  of  a  process  when  carried  out  in  one  way,  is  known,  its 
value  when  the  process  is  carried  out  in  any  other  way  is  also  known. 
If,  for  example,  the  maximum  osmotic  work  which  a  process  is 
capable  of  producing  is  known,  then  the  maximum  quantity  of  elec- 
trical energy  which  may  be  obtained  from  it  is  also  known.  When,  \ 
further,  the  quantity  of  substance,  and  so  the  quantity  of  electricity, 


ELECTROMOTIVE   FORCE 


161 


involved  is  known,  the  electromotive  force  may  at  once  be  calculated 
with  the  aid  of  Faraday's  law  as  follows  :  — 

Electromotive  force  x  Quantity  of  electricity  =  Electrical  energy 

TT  TT.I  *.-      £  Electrical  energy 

Hence  Electromotive  force  =  -^ -r- ^—. — .  .  . .    . 

Quantity  of  electricity 

From  the  above  discussion,  it  is  evident  how  important  it  is, 
especially  for  the  calculation  of  electromotive  forces,  to  know  the 
maximum  external  work  obtainable  from  an  isothermal  process. 
Such  knowledge  will  be  applied  later  on  in  the  book.  The  second 
law  of  energetics  may  also  be  stated  in  the  following  form  :  — 

TJie  sum  of  the  quantities  of  work  involved  in  the  different  parts  of 
an  isothermal,  reversible,  cyclical  process  is  equal  to  zero. 

It  is  also  of  great  importance  in  electro-chemistry  to  know  the 
maximum  quantity  of  work  obtainable  when  a  given  quantity  of 
heat  is  lowered  from  one  temperature  to  another ;  for  this,  too,  is  a 
spontaneous  process.  In  order  to  find  this  quantity  of  work,  it  is 
necessary  to  devise  a  process  by  means  of  which  heat  may  be  trans- 
ferred reversibly  from  one  temperature  to  another  which  is  lower. 
Such  a  process  is  easily  found.  As  the  machine  or  carrier  of  heat 
from  the  one  temperature  to  the  other  a  perfect  gas  may  be  used.  In 
this  case  the  calculation  is  especially  simple.  It  is  only  necessary  to 
be  able  to  determine  the  quantity  of  work  ob- 
tainable when  a  gas  of  a  volume  v  and  pressure  p 
changes  isothermally  to  a  volume  v'  and  pressure 
p'.  This  quantity  of  work  is  the  same  as  that 
obtainable  when  an  "  ideal "  solution  of  a  volume 
V  and  osmotic  pressure  P  changes  isothermally 
to  the  values  V  and  P  respectively.  As  fre- 
quent use  of  osmotic  work  will  be  made,  the  fol- 
lowing derivation  is  of  twofold  interest. 

If  in  the  apparatus  shown  in  Figure  34  one 
mol  of  a  saturated  vapor  (in  contact  with  its 
liquid)  of  volume  v  and  pressure  p  be  allowed 
to  expand  against  the  constant  pressure  p  until 
the  volume  v'  is  reached,  the  maximum  work 
obtainable  is  easily  calculated.     If  it  be  imagined  that  the  increase 
in  volume  (v1  —  v)  is  divided  into  infinitely  small  parts  designated 
by  dv,  then  the  work  obtainable  during  each  successive  expansion  of 
dv  is  equal  to  pdv,  and  the  total  work, 


9 

,-v 

V 

VAPOR 

^"-LIQUID  =^= 

FIG.  34 


w= 


dv. 


168  A  TEXT-BOOK   OF   ELECTRO-CHEMISTRY 

Expressed  in  words,  the  total  work  is  equal  to  p  times  the  sum  of 
these  infinitely  small  volumes  dv  from  the  value  v  to  that  of  v'.  Con- 
sequently 

W=p(v'-v). 

Attention  is  here  called  to  page  4  of  the  introduction,  where  it  is 
shown  that  the  product  pv,  and  therefore  p(v'  —  v)  or  pv",  represents 

a  quantity  of  work  [and  also  to 
Figure  35,  which  is  a  graphical 
representation  of  the  relation  of 
p,  v'  —  v,  and  W]. 

In  the  case  now  to  be  consid- 


WORK 


ered,  the  relations  are  not  quite  so 
simple,  since  the  pressure,  instead 
of  remaining  constant  as  in  the 

above    case,   continually    changes 

v    2v  v        with  the  volume  until  it  reaches 

the  value  p'.     We  have  not  then 

merely  to  add  together  the  values  of  dv;  the  sum  of  the  endless 
number  of  infinitely  small  quantities  of  work  pdv  must  be  found, 
where  the  value  of  p  is  no  longer  a  constant  but  a  function  of  v,  or 
in  other  words,  where  the  value  of  p  depends  upon  and  varies  with 
the  value  of  v.  The  quantity  of  work  involved  during  the  change 
in  volume  and  pressure  of  the  perfect  gas  is  given  by  the  equation, 


XV' 
pdv. 


W 

The  values  of  p  and  v  are  dependent  upon  each  other  in  a  definite 
and  known  manner.  For  one  mol  of  a  gas,  the  following  equation 
holds  (see  page  53)  :  — 


RT 

or  p  =  -- 

v 


By  substituting  this  value  of  p  in  the  above  equation  and  placing 
the  constants  before  the  sign  of  summation  (the  integral  sign),  the 
following  equation  is  obtained  :  — 


There  is  here  only  one  variable,   and  the  integral  is  determinable. 
From  integral  calculus  it  is  known  that 


ELECTROMOTIVE   FORCE 


169 


1 v1 
log    ' 


v          v'          0.4343  ™&v 

where   In   signifies  the   natural   and   log   the  ordinary  logarithm; 
consequently 

W: 


Since,  according  to  the  gas  law  of  constant  pressure-volume  product 
(Boy  le-Mari  otte), 

v'  —P 

i  > 
v      p 

the  above  equation  may  also  be  written  as  follows :  — 


It  is  evident,  from  the  above  equation,  that  the  available  work  is 
proportional  to  the  absolute  temperature  of  the  gas,  and  further, 
that  it  does  not  depend  upon  the  absolute  values  of  the  pressure 
or  volume,  but  upon  the  relation  between  the  respective  values  of 
each.  Accordingly,  the  quantity  of  available  work  is  the  same 
whether  the  gas  passes  from  a  pressure  of  ten  to  a  pressure  of  one 
atmosphere,  or  from  a  pressure  of  one  to  a  pressure  of  one  tenth  of 
an  atmosphere. 

It  may  be  recalled  that  when  it  is  desired  to  express  the  work  in 

mean  gram-calories,  the  value  of  ^  =  1.985, 
gram-centimeters,     the  value  of  E  =  84800  (approx.),  and  in 
joules,  the  value  of  R  =  8.32. 

[The  relation  between  the  pressure  and  volume  changes  and  the 
maximum  quantity  of  work  obtain- 
able during  an  isothermal  expan- 
sion of  a  gas  is  shown  graphically 
in  Figure  36.  The  line  ab  is  the 
pressure-volume  curve  and  the 
area  abw'  represents  the  work 
done  by  the  gas  in  expanding  from 
the  volume  v  to  v'  at  constant 
temperature.  In  the  above  math- 
ematical derivation  of  the  equa- 
tion representing  the  work,  there- 
fore, this  area  has  been  found  by  obtaining  the  sum  of  the  infinitely 
small  areas  pdv  of  which  it  is  composed.] 


170 


A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 


If  one  mol  of  a  gas  expands  so  that  its  pressure  decreases  to  one 
hundredth  of  its  original  value,  or,  what  is  the  same,  its  volume 
increases  a  hundred  fold,  the  maximum  quantity  of  work  obtainable 
from  the  process  at  17°  t  or  290°  T  is  given  by  the  following  equa- 
tions :  — 

Sram-calories> 


or 


84800^290 


100 


gram-centimeters. 


If,  instead  of  one  mol,  n  mols  of  gas  had  been  taken,  the  quantity  of 
work  obtainable  would  have  been  n  times  as  great. 

It  may  be  well  to  remark  that  this  work  which  is  obtained  during 
the  isothermal  expansion  of  a  gas  is  not  taken  from  the  internal 
energy  of  the  gas  itself,  but  from  the  heat  energy  of  the  surround- 
ings. The  gas  serves  only  as  a  medium  for  the  transformation  of 
heat  into  work. 

It  is  now  possible  for  us  to  consider  the  process  for  the  reversible 
transference  of  heat  from  one  temperature  to  another,  and  to  calcu- 
late the  quantities  of  work  involved  in  the  different  parts  of  the 
process. 

PART  1.  One  mol  of  the  gas  is  compressed  reversibly  at  the  tem- 
perature T  from  a  volume  v'  to  the  volume  v.  The  work  done  upon 
the  gas  is  given  by  the  equation 


This   quantity  of  work  is  converted  into   heat,  which  is  absorbed 
by  the  surroundings.     Moreover,  the  quantity  of  heat  thus  set  free 

is,  according  to  the  first  law  of 
energetics,  equivalent  to  the  work 
done,  or 


[This  quantity  of  heat  and  of  work 
is  represented  in  Figure  37  by  the 
area  ctbv'v.'] 

PART  2.  The  gas  is  now  brought 
FIG.  37  into  surroundings  of  a  tempera- 

ture   T+dT.      The   quantity   of 

heat  thereby  absorbed  by  the  gas  is  negligibly  small  as  compared 
with  Q,  and,  moreover,  the  same  quantity  is  given  off  to  the  sur- 


ELECTROMOTIVE   FORCE  171 

roundings  in  a  later  part  of  the  process.  Since  the  volume  v  of  the 
gas  remains  constant  during  the  change  in  temperature,  no  exter- 
nal work  is  done.  [This  change  is  represented  by  the  line  be  in 
Figure  37.] 

PART  3.   At  the  new  temperature,  the  gas  is  expanded  reversibly 
from  volume  v  to  volume  v'.    The  work  done  by  the  gas  is,  then, 


A  quantity  of  heat  equivalent  to  this  work  is  absorbed  from  the 
surroundings,  — 

-  +  RdT\n-> 


and  Q3  are  represented  by  the  area  cdv'v.] 

PART  4.  Finally,  the  gas  is  brought  into  surroundings  of  a  tem- 
perature T.  After  the  same  negligible  quantity  of  heat  as  was 
absorbed  in  part  2  has  been  given  out  to  the  surroundings,  the 
process  has  passed  along  the  line  da  to  a,  and  the  gas  is  in  its  origi- 
nal condition.  The  process  is  now  complete. 

As  a  final  result  of  the  whole  process,  it  is  evident  that  the 
quantity  of  work  W  obtained  is  as  follows  :  — 


[Kef  erring  to  the  figure,  W  is  seen  to  be  equal  to  the  area  a&cd] 
An  equivalent  quantity  of  heat  has  therefore  been  transformed  into 
work,  but  at  the  same  time  the  quantity  of  heat 


v' 


KTln- 

v 


has  disappeared  at  the  temperature  T+dT,  and  been  recovered  at 
the  temperature  T.  Here  there  are  two  different  kinds  of  heat 
transformations  taking  place  simultaneously.  A  definite  quantity 
of  heat  Q'  can  only  be  transformed  into  work  by  a  reversible-cyclical 
process  operating  between  the  temperatures  T+dT  and  T  when 
another  definite  quantity  of  heat  Q  passes  from  the  higher  to  the 
lower  of  these  two  temperatures.  The  following  equation  gives  the 
relation  which  exists  between  these  two  quantities  of  heat  :  — 


The  result  of  the   above   deduction  is  of    general    application. 


172  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

Whenever  a  quantity  of  heat  is  transferred  from  a  higher  to  a  lower 
temperature,  and  no  other  change  in  state  takes  place,  only  a  frac- 
tion of  it  can  in  any  case  be  transformed  into  work.  The  relation 
between  this  fraction  and  the  rest  of  the  heat  when  the  maximum 
quantity  of  work  is  obtained  is  given  by  the  above  equation. 

Let  us  apply  these  considerations  to  the  reversible  galvanic  ele- 
ments. If  the  heat  evolved  by  the  reactions  taking  place  within 
such  an  element,  having  no  internal  resistance,  be  entirely  changed 
into  electrical  energy  while  the  element  is  immersed  in  a  calorimeter, 
no  heating  effect  would  be  observed.  The  reason  is  that  just  as 
much  energy  as  was  produced  would  be  consumed  as  electrical 
energy  (capable  of  transformation  into  work)  in  the  external  circuit. 
As  a  matter  of  fact  this  simple  relation  very  seldom  exists,  and 
therefore  a  generation  of  heat  in  the  calorimeter  can  usually  be 
observed. 

Imagine  a  reversible  cell  of  electromotive  force  F  at  the  tempera- 
ture Ty  and  suppose  the  quantity  of  electricity,  96,540  coulombs,  or 
Q,  be  passed  through  it,  then  the  maximum  electrical  energy  which 
may  be  produced  is  FQ.  Let  Q  be  the  sum  of  the  heats  of  the 
corresponding  reactions.  The  action  of  the  cell  is  attended  by 
absorption  of  heat,  the  heat  absorbed  being  FQ  —  Q,  according  to 
the  first  law  of  energy.  Suppose  the  temperature  increased  by  dT 
and  the  amount  of  electricity  Q  again  sent  through  the  cell,  but  in 
the  opposite  direction,  and  under  the  new  electromotive  force, 
F  +  <?F  ;  the  amount  of  work  thus  consumed  will  be  Q(F  -f  C£F).  The 
corresponding  sum  of  the  heat  of  reaction  in  this  reversed  process 
has  changed  but  little,  and,  neglecting  this  change,  is  Q  +  dQ.  The 
heat  generated  in  the  cell  is  in  this  case  equal  to  the  difference  be- 
tween the  electrical  energy  used  and  the  heat  taken  up  in  the  chem- 
ical processes,  and  is  thus  equal  to  FQ  +  qdF  —  (Q  -f  dQ).  If  the 
element  be  brought  again  to  the  temperature  T,  it  is  once  more  in 
its  original  condition. 

As  the  end  result  of  the  process,  the  work  Q^F  has  been  per- 
formed, and  accordingly  the  equivalent  amount  of  heat  Q^F  pro- 
duced. At  the  temperature  T  the  heat  F—  Q  Q  has  been  lost,  but  at 
T  +  dT  the  heat  FQ  +  QC£F  —  (Q  -f-  dQ)  has  been  obtained,  which 
with  slight  error  may  be  simplified  to  QF  +  QdF  —  Q.  As  QC?F  is 
derived  from  the  work  done,  the  amount  of  heat  FQ  —  Q  has  been 
raised  from  the  temperature  T  to  T  -f  dT.  Conversely,  in  order  to 
change  the  quantity  of  heat  QC£F  into  work,  the  amount  of  heat 
QF  —  Q  must  fall  from  the  temperature  T  +  dTto  T,  consequently 
the  following  expressions  are  correct  in  accordance  with  page  171 :  — 


ELECTROMOTIVE   FORCE  173 

flT 
QdF=(FQ-Q)^;  (1) 

*9  -  Q  =  S^i  (2) 

>-f  +  r£-  (3) 

Since  we  can  calculate  Q  from  thermochemical  data,  or  can  deter- 
mine it  directly,  we  are  able,  with  the  help  of  the  experimentally 
determined  temperature  coefficient  of  the  electromotive  force,  to 
calculate  the  maximum  electrical  energy  obtainable,  or  the  electro- 
motive force  of  the  cell.  In  the  thermochemical  data  the  numbers 
always  apply  to  a  gram  equivalent  or  gram-molecule,  the  heat  gener- 
ated being  considered  positive. 

If  the  temperature  coefficient  is  positive,  i.e.  if  the  electromotive 
force  increases  with  rise  of  temperature,  it  follows  from  equation 
(2)  that  FQ  is  greater  than  Q:  the  cell  in  activity  tends  to  be- 
come cooler,  and  so  takes  heat  from  the  surroundings.  If,  on  the 
other  hand,  the  temperature  coefficient  is  negative,  FQ  is  less  than  Q, 
and  the  cell  becomes  warmer.  If  finally  the  temperature  coeffi- 
cient is  zero,  the  heat  of  reaction  is  simply  and  completely  trans- 
formed into  electrical  energy,  and  the  cell  itself  exhibits  no  ther- 
mal change.  This  latter  condition  is  nearly  realized  in  the  Daniell 
cell. 

It  is  necessary  to  emphasize  this  fact  that  the  heat  of  the  chemical 
reactions  is  not  a  strict  measure  of  the  available  electrical  energy  of 
a  reversible  element,  although  experience  has  shown  that  in  many 

d,Y 
cases  it  enables  us  to  estimate  it  approximately,  since  —  is  very 

often  negligible  as  compared  with  Q,  and  therefore  may  be  omitted 
from  equation  (3). 

The  above  formula  of  Helmholtz  has  been  qualitatively  proven 
by  Czapski  and  Gockel,  and  quantitatively  by  Jahn  and  others.  Sev- 
eral apparent  contradictions,  as  later  shown  by  Nernst,  arose  from 
erroneously  assumed  values  for  the  heat  of  formation  of  mercury 
compounds. 

For  illustration,  the  values  found  by  Jahn1  and  Bugarszky2 
are  given  in  the  table  on  the  next  page. 

In  the  table,    F   denotes  the   electromotive  force   at  0°,—    the 

1  Wied.  Ann.,  50,  189  (1893). 
*Ztschr.  anorg.  Chem.,  14,  145  (1897). 


174 


A   TEXT-BOOK  OF  ELECTRO-CHEMISTRY 


change  in  electromotive  force  per  degree,  2  FQ  the  electrical 
energy  given  out  by  the  cell  when  two  equivalents  of  the  substances 
have  reacted,  and  Hr  the  heat  of  reaction  for  the  same  quantities  of 
the  reacting  substances,  expressed  in  calories.  In  the  last  two 
columns  are  given  the  values  of  the  heat  effect  in  the  cell,  i.e.  those 

calculated  from  —  and  from  the  expression,  Q  —  2  FQ,  respectively. 


CELL 

F,ATO° 

dv 
dT 

2   FQ 

Hr 

HEAT  EFFECT  IN  CELL 

CALO. 

Q—   2    FQ 

Cu     CuS04  4-  100  H2O 

1.0962 
1.015 
0.828 

0.1483 
t=18.5° 

+0.000034 
-0.000402 
-0.000105 

4-0.000837 

50526 
46907 
38276 

7566 

50110 
52046 
39764 

-3280 

-428 
+  5082 
4-1326 

-  11276 

-416 
4-5139 
4-1488 

-  1084& 

Zn    ZnSO*  4-  100  H2O            ' 

As    AeCl 

Zn    ZnCl2  4  100  HoO-           J 

AST    AffBr- 

•**&     •rv&-LjA-                                I 
Zn—  ZnBr2  4-  25  H20.              1 

Hg-HgCl  +  KC1,  O.OlCn—  , 
1  Cw,  KN03 
Hg-Hg20  4-  KOH,  0.01  C~  ' 

As  is  evident,  the  agreement  between  the  heat  value  of  the  cell 
as  observed  in  the  calorimeter  and  that  calculated  from  the  differ- 
ence between  the  electrical  energy  produced  by  the  current  and  the 
corresponding  heat  of  reaction  is  satisfactory  in  each  case.  The 
last  set  of  measurements  is  particularly  interesting,  since  the  chemical 
process  which  spontaneously  gives  rise  to  the  electric  current  is 
endothermic  and  the  cell  when  in  operation  absorbs  heat  from  the 
surroundings.  It  furnishes  a  striking  proof  of  the  incorrectness  of 
the  assumption  that  the  heat  of  reaction  is  a  measure  of  the  work 
obtainable  from  a  cell. 

The  above  equations  have  also  been  found  to  hold  for  cells  of  fused 
electrolytes  at  high  temperature. 

It  may  be  advisable  to  add  that  electrical  energy  may  be  measured 
by  inserting  the  cell  in  a  circuit,  the  resistance  of  which  is  so  great 
that  internal  resistance  of  the  cell  is  negligible  in  comparison. 
The  electrical  energy  being  allowed  to  change  into  heat,  the 
amount  of  the  latter  generated  in  the  unit  of  time  is  C2R,  ac- 
cording to  Joule's  law  (page  18),  where  R  represents  the  resist- 
ance of  the  circuit,  and  c  the  current-strength.  Knowing  the  resist- 
ance R,  and  having  measured  the  current-strength,  the  quantity  of 
electrical  energy  produced  per  unit  time  may  be  calculated.  From 
this  the  quantity  of  energy  produced  when  96,540  coulombs,  or  twice 


ELECTROMOTIVE   FORCE  175 

that  number,  pass  through  the  circuit  may  be  easily  determined,  the 
choice  between  these  numbers  depending  upon  whether  one  or  two 
gram  equivalents  of  the  substances  take  part  in  the  chemical  reac- 
tion. As  the  internal  resistance  of  the  cell  itself  is  negligible  com- 
pared to  the  external,  the  electrical  heat  effect  produced  within  the 
cell  is  insignificant,  and  may  be  left  out  of  consideration.  The  heat 
generated  in  the  cell,  and  measured  in  a  calorimeter  as  previously 
described,  has  nothing  to  do  with  the  electrical  heat  effect,  c2R, 
which  is  the  heat  generated  by  the  electric  current  and  hence  a 
measure  of  the  electrical  energy  furnished  by  the  cell.  It  is,  instead, 
equal  to  the  difference  between  the  heat  of  the  reactions  which  take 
place  in  the  cell  and  the  electrical  heat  effect  just  mentioned. 

The  equation  previously  derived  enables  us  to  determine  the 
electromotive  force  of  a  cell  from  a  knowledge  of  its  temperature 
coefficient  and  of  the  heat  of  reaction.  The  electromotive  force  of 
reversible  cells  may  be  determined  in  another  manner,  as  already 
indicated  on  page  166.  Before  proceeding  with  the  calculation,  a 
clear  idea  of  the  concept,  electrolytic  solution  tension,  which  was  intro- 
duced by  Nernst,  is  necessary.1  We  will,  however,  follow  Ostwald's 
nomenclature  and  call  it  electrolytic  solution  pressure. 

Electrolytic  Solution  Pressure.  —  The  expression  "  vapor  pressure 
of  a  substance  "  is  one  commonly  understood.  It  signifies  the  tend- 
ency of  a  substance  to  enter  the  gaseous  state. 
If,  for  example,  we  allow  water  at  a  certain  tem- 
perature to  evaporate  in  a  long  cylindrical  vessel, 
as  shown  in  Figure  38,  in  which  there  is  a  mov- 
able air-tight  piston,  and  if  a  pressure  p'  is  exerted 
upon  the  piston  less  than  the  vapor  pressure  of  the 
water,  the  piston  is  moved  upwards  and  more 
water  evaporates.  Hence  a  condition  of  equilib- 
rium is  only  established  when  a  certain  definite 
pressure  equal  to  p  is  exerted  upon  the  piston  FIG<  33 

from  without.  The  latter  will  then  remain  station- 
ary in  whatever  position  it  be  placed  as  soon  as  equilibrium  between 
water  and  vapor  obtains.  If  the  pressure  on  the  piston  be  slightly 
increased,  the  piston  will  fall  and  all  of  the  vapor  will  condense  to 
water ;  if,  on  the  other  hand,  it  be  slightly  diminished,  the  piston 
will  rise  and  all  of  the  water  will  vaporize.  The  pressure  downward 
on  the  piston  at  equilibrium  represents  the  vapor  pressure  of  water 
at  the  temperature  of  the  experiment. 

The  "solution  pressure"  of   a  substance,  for  example  sugar,  is 
1  Ztschr.  phys.  Chem.,  4,  129  (1889). 


Water 


176  A   TEXT-BOOK  OF   ELECTRO-CHEMISTRY 

spoken  of  just  as  is  the  vapor  pressure,  and  thereby  is  meant  its 
tendency  to  pass  into  the  dissolved  state.  This  pressure  may  be 
measured  in  a  manner  similar  to  the  measurement  of  vapor  pres- 
sure. A  diagram  of  the  apparatus  is  shown  in  Figure  39.  At  the 
bottom  of  the  vessel  there  is  an  excess  of  the 
solid  substance,  over  which  is  its  saturated  solution, 
and  a  semipermeable  piston,  that  is,  one  which 
is  permeable  to  the  water  but  not  to  the  dissolved 
substance.  Above  the  piston  is  pure  water. 
If  the  piston  be  weighted,  the  magnitude  of  the 
load  determines  the  direction  in  which  the  piston 
will  move.  If  the  load  be  less  than  the  pressure 
derived  from  the  dissolved  particles,  the  "  osmotic 
pressure,"  the  piston  will  rise  and  water  penetrate 
into  the  solution,  which  being  thereby  diluted,  al- 
lows more  of  the  solid  substance  to  be  dissolved.  If  it  be  greater,  the 
piston  sinks,  and  water  passes  from  the  solution.  The  latter  becoming 
supersaturated,  some  of  the  solid  substance  separates  out  again. 
Under  a  certain  weight  the  condition  of  equilibrium  must  exist  and 
the  piston  remain  stationary  at  any  part  of  the  cylinder.  Evidently 
the  relations  are  here  exactly  analogous  to  those  of  the  vapor  pres- 
sure of  water,  and  the  magnitude  of  the  solution  pressure  of  the 
substance  at  a  given  temperature  is  measured  by  the  weight  on  the 
piston  when  in  a  condition  of  equilibrium. 

It  may  here  be  repeated  that,  as  made  evident  through  these  con- 
siderations, the  vapor  pressure  of  water  being  that  pressure  exerted 
by  the  vapor  in  contact  with  water,  that  is,  the  "  saturated " 
vapor,  so  also  the  "  solution  pressure  "  of  a  substance  is  the  osmotic 
pressure  of  the  solution  which  is  in  equilibrium  with  the  substance, 
that  is,  the  "  saturated  "  solution. 

This  conception  may  finally  be  applied  to  the  passing  of  sub- 
stances, chiefly  in  the  case  of  elements,  and  especially  metals,  into 
the  ionic  condition.  Hydrogen  and  the  metals  are  capable  of  form- 
ing only  positive  ions ;  chlorine,  bromine,  iodine,  etc.,  on  the  con- 
trary, form  only  negative  ions.  The  magnitude  of  this  "electro- 
lytic solution  pressure  "  may  be  conceived  as  determined  in  exactly 
the  same  manner  as  the  ordinary  solution  pressure.  We  imagine 
the  substance  in  contact  with  water  saturated  with  the  ions  in  ques- 
tion, under  a  similar  piston,  which  separates  the  saturated  solution 
from  the  water,  and  is  impermeable  for  the  ions.  The  equilibrium 
with  the  osmotic  pressure  of  the  ions  will  be  brought  about  by  a 
certain  weight  of  the  piston,  and  no  ions  will  enter  the  solution 


ELECTROMOTIVE   FORCE  177 

from  the  substance  nor  pass  out  of  solution.  The  weight  of  the 
piston  in  equilibrium  represents  the  value  of  the  electrolytic  solution 
pressure,  which  is  usually  represented  by  P,  and  also  expresses  the 
equally  great  and  oppositely  directed  osmotic  pressure  of  the  ions. 
This  method  is  practically  inapplicable,  because  in  no  case  can 
appreciable  amounts  of  positive  or  negative  ions  alone  come  into 
existence ;  this  does  not,  however,  affect  the  value  of  the  conception. 

In  order  to  explain  the  production  of  a  potential-difference 
through  the  contact  of  a  solid  substance  with  a  liquid,  imagine  a 
metal  dipped  into  pure  water,  and  that  a  certain  amount  of  metal 
ions  is  produced  owing  to  the  electrolytic  solution  pressure.  The 
metal  at  the  same  time  becomes  negatively  electrified,  since  both 
kinds  of  electricity  must  be  simultaneously  produced  whenever 
electrical  energy  conies  into  existence.  The  solution  is  thus  posi- 
tively electrified  and  the  metal  negatively,  and 
there  is  formed  a  so-called  double-layer  ("  Dop- 
pelschicht ")  of  electricities  of  opposite  signs. 
[This  is  represented  in  Figure  40,  in  which  the 
positive  and  negative  ions  are  represented  by 
plus  and  minus  signs,  respectively.] 

The  ions  sent  into  the  solution  with  positive 
charges  and  the  negatively  charged  metal  at- 
tract each  other;  in  other  words,  a  potential- 
difference  is  produced.  The  solution  pressure  FIG.  49 
constantly  tends  to  send  more  ions  into  solu- 
tion, while  the  electrostatic  attraction  of  the  electrical  double-layer 
opposes  this  action,  and  evidently  equilibrium  is  reached  when  the 
opposing  tendencies  are  equal.  Since  the  ions  have  very  high 
charges  of  electricity,  this  condition  of  equilibrium  occurs  before 
weighable  quantities  of  the  ions  have  passed  into  the  water.  In  the 
case  of  pure  water  the  potential-difference,  or  strength  of  the  elec- 
trical double-layer,  depends  only  upon  the  magnitude  of  the  solution 
pressure,  but  if  the  metal  be  in  a  solution  of  one  of  its  salts,  another 
factor  is  introduced,  due  to  the  metal  ions  already  present.  The 
osmotic  pressure  of  these  ions  opposes  the  entrance  of  new  ions  of 
the  same  kind.  It  may  occur  that  this  osmotic  pressure  is  exactly 
in  equilibrium  with  the  electrolytic  solution  pressure  of  the  metal, 
consequently  the  latter  will  yield  no  ions  and  will  not  become  nega- 
tively charged ;  in  short,  under  these  circumstances  there  will  be  no 
electrical  double-layer  produced.  The  nature  of  the  negative  ions 
of  the  salt  in  solution  has  no  influence. 

If  the  osmotic  pressure  of  the  metal  ions  differs  from  the  electri- 


178  A    TEXT  BOOK  OF  ELECTRO-CHEMISTRY 

cal  solution  pressure,  two  different  cases  may  be  distinguished 
according  as  the  former  or  the  latter  is  the  greater.  In  the  second 
case,  ions  pass  from  the  metal  into  the  solution  as  in  pure  water, 
and  an  electrical  double-layer  results.  This  action  would  evidently 
not  be  as  great  as  in  pure  water,  since  so  many  ions  cannot  enter 
the  solution,  owing  to  the  fact  that  the. electrolytic  solution  pressure 
is  opposed  by  the  osmotic  pressure  of  the  ions  already  present. 
The  quantities  here  involved  are  shown  by  the  calculation  made  by 
Kriiger.1  In  the  case  of  zinc  which  is  dipped  in  a  solution  which  is 
of  normal  concentration  in  respect  to  Zn  ions,  3.10~9  grams  per  square 
centimeter  go  into  solution.  In  the  other  case  ions  separate  from  the 
solution  and  are  precipitated  upon  the  metal,  communicating  their 
positive  electric  charges  to  it.  The  metal  thus  becomes  positively 
electrified,  the  solution,  which  formerly  contained  equivalent  amounts 
of  positive  and  negative  ions,  negatively  electrified,  and  again  the 
electrical  double-layer  is  produced,  the  attraction  of  which  opposes 
the  previously  superior  osmotic  pressure  and  adds  itself  to  the  solu- 
tion pressure.  This  proceeds  until  the  condition  of  equilibrium  is 
reached.  Here  also  the  quantity  of  ions  which  is  precipitated  is 
unweighable.  The  strength  of  the  electrical  double-layer  and  the 
electrostatic  attraction  due  to  it  is  evidently  dependent  upon  the 
osmotic  pressure  of  the  metal  ions  in  the  solution. 

In  all,  three  cases  must  then  be  distinguished :  — 

First,  when  P  =  P, 

where  P  is  the  electrolytic  solution  pressure  and  P  the  osmotic  pres- 
sure of  the  metal  ions  under  consideration.  Here  equilibrium 
exists  and  no  potential-difference  or  electrical  double-layer  is  formed 
between  solution  and  metal. 

Second,  when  P  >  P. 

In  this  case,  the  metal  possesses  a  negative  and  the  solution  a 
positive  charge  of  electricity.  The  electrostatic  attraction  opposes 
the  solution  pressure. 

Third,  when  p  <  P. 

Here  the  metal  possesses  a  positive  and  the  solution  a  negative 
charge.  The  electrostatic  attraction  is  superposed  on  the  solution 
pressure. 

On  turning  our  attention  to  the  actual  experimental  facts,  it  is 
found,  as  will  be  seen  later,  that  such  base  metals  as  the  alkali 
metals,  zinc,  cadmium,  cobalt,  nickel,  and  iron,  are  always  nega- 
tively charged  when  placed  in  solutions  of  their  salts ;  the  solution 

1  Ztschr.  phys.  Chem.,  35,  18  (1900). 


ELECTROMOTIVE   FORCE 


179 


pressure  in  these  cases  is  so  great  that,  owing  to  the  limited  solu- 
bility of  the  salts,  the  osmotic  pressure  of  the  metal  ions  can  never 
be  raised  to  equilibrium  with  the  solution  pressure.  On  the  other 
hand,  with  the  noble  metals,  silver,  mercury,  etc.,  the  metal  is 
usually  positively  electrified  in  solutions  of  its  salts.  The  solution 
pressure  of  the  metals  is  here  slight,  and  it  is  only  by  employing 
solutions  containing  very  few  of  the  ions  in  question,  i.e.  such'  as 
have  very  low  osmotic  pressure  due  to  these  ions,  that  it  is  possible 
to  have  the  metal  negatively  charged  in  the  solution. 

With  such  substances  as  produce  negative  ions,  e.g.  chlorine,  there 
is  complete  analogy.  If  the  osmotic  pressure  of  the  chlorine  ions  is 
greater  than  the  electrolytic  solution  pressure,  ions  pass  into  the 
condition  of  ordinary  chlorine,  and  the  "chlorine  electrode"  becomes 
negatively  charged.  In  the  other  case 
the  electrode  becomes  positively  charged. 
As  a  matter  of  fact,  as  far  as  we  know, 
all  substances  which  produce  negative 
ions  have  high  solution  pressures. 

So  far  the  electrolytic  solution  pres- 
sure of  a  substance  has  been  referred  to 
as  if  it  were  a  constant,  but,  just  as  with 
the  vapor  pressure  and  ordinary  solution 
pressure,  it  is  only  constant  under  cer- 
tain conditions,  i.e.  only  when  the  tem- 
perature and  the  concentration  of  the 
electrode  substance  in  question  remains 
unaltered. 

It  is  well  known  that  the  vapor  pres- 
sure of  water  changes  greatly  with  the 
temperature;  but  that  it  is  affected  by 
the  concentration  or  density  of  the  water  itself,  and  is  higher  the 
greater  this  concentration,  may  be  less  commonly  recognized.  The 
fact  may  be  recalled  that  if  two  open  vessels  containing  water  at 
different  heights  be  allowed  to  stand  in  a  confined  space,  the  water 
distills  from  the  higher  level  to  the  lower.  The  water  in  each  ves- 
sel is  under  the  pressure  of  the  vapor  above  it,  and  these  columns  of 
vapor  differ  in  height  by  the  difference  between  the  levels  of  the 
water  surfaces.  Consequently  the  system  is  not  in  equilibrium,  the 
tendency  being  for  vapor  to  condense  under  the  greater  pressure  and 
be  generated  under  the  lower,  which  process  continues  until  the  sur- 
faces of  the  water  in  the  two  vessels  are  at  the  same  level,  or  that 
in  one  of  the  vessels  is  exhausted. 


FIG.  41 


180  A   TEXT-BOOK  OF   ELECTRO-CHEMISTRY 

In  the  accompanying  figure l  the  pure  water  and  any  water  solu 
tion  are  separated  by  a  membrane  permeable  to  the  water  only. 
Under  the  conditions  represented  the  liquids  are  in  osmotic  equi- 
librium, but  the  vapor  pressure  p±  at  the  surface  of  the  solution  is 
less  than  that  p  of  the  water,  and  the  equation  pl  +  w=p  must 
represent  the  existing  condition,  where  w  is  the  weight  of  the  column 
of  vapor  whose  height  is  equal  to  the  difference  in  level  between  the 
two  liquids.  If  this  were  not  true,  water  would  distill  from  one  sur- 
face to  the  other,  thereby  destroying  the  existing  condition  of  osmotic 
equilibrium,  and  would  also  pass  through  the  membrane  in  one 
direction  in  order  to  reproduce  the  osmotic  equilibrium,  etc.  In 
short,  a  perpetual  motion  would  result,  by  which  an  unlimited 
amount  of  the  heat  of  the  surroundings  at  constant  temperature  could 
be  transformed  into  work  (through  the  distillation  of  water  vapor). 
This  conflicts  with  the  second  law  of  energetics,  and  therefore  is 
impossible. 

If  the  upper  end  of  the  tube  be  closed  by  a  membrane,  allowing 
the  passage  of  water  vapor  only,  and  a  quantity  of  a  gas  insoluble 
in  the  liquid  be  placed  between  this  membrane  and  the  surface  of 
the  liquid,  it  will  exert  a  certain  pressure  upon  the  latter,  which 
will  consequently  sink  to  a  lower  level.  The  conditions  of  the 
equilibrium  must  again  be  that  the  vapor  pressure  pj  at  the  surface 
of  the  solution,  increased  by  the  pressure  of  the  column  of  water 
vapor  d'  between  the  two  levels,  is  equal  to  the  vapor  pressure  of 
the  pure  water  p,  or  pj  +  w1  —p.  Evidently  p  has  remained  unal- 
tered, d'  is  less  than  d,  therefore  PI  is  greater  than  p^  that  is,  at 
the  "  compressed "  surface,  where  the  water  is  at  the  greater  con- 
centration, there  is  a  higher  vapor  pressure  than  when  the  water  is 
under  a  lower  external  pressure.  The  increase  in  the  vapor  pres- 
sure is  evidently  proportional  to  the  pressure  acting  on  the  surface.2 

Of  the  ordinary  solution  pressure  it  is  also  known  that  the  con- 
centration of  the  substances  plays  an  important  part.  This  is 
shown  by  Henry's  law,  in  accordance  with  which  the  solubility  of 
a  gas,  and  therefore  its  solution  pressure,  since  the  two  are  synony- 
mous, is  to  a  great  extent  dependent  upon  the  pressure,  in  other 
words,  upon  the  concentration  j  it  is,  in  fact,  nearly  proportional  to 
the  latter. 

1  Ztschr.  phys.  Chem.,  3,  115  (1889). 

2  This  conclusion  was  established  by  the  work  of  Des  Coudres  and  the  author, 
which  preceded  the  appearance  of  the  article  of  Schiller  on  the  same  subject 
(Wied.  Ann.,  53,  396,  1894).     The  experiments  in  connection  therewith  were 
unavoidably  interrupted  and  never  concluded. 


ELECTROMOTIVE   FORCE  181 

What  has  been  said  of  vapor  pressure  and  solution  pressure  applies 
equally  well  to  electrolytic  solution  pressure,  and  accordingly  there 
are  cells  possessing  certain  electromotive  forces  dependent  only 
upon  the  different  concentrations  of  the  same  ion-producing  sub- 
stances. It  is  true  that  usually  but  one  condition  of  concentration 
for  solid  substances  is  recognized,  and  consequently  only  a  single 
definite  electrolytic  solution  pressure.  But  even  here  the  concentra- 
tion will  be  varied,  as  will  be  later  described. 

As  in  the  case  of  the  solubility,  so  the  electrolytic  solution  pres- 
sure changes  with  a  change  in  solvent.  However,  it  has  been  shown 
by  Luther 1  that  the  relations  between  the  solution  pressures  of  various 
metals  are  independent  of  the  nature  of  the  solvent,  and,  moreover, 
always  possess  the  same  value. 

The  electrolytic  solution  pressure  varies  with  the  temperature. 

Calculation  of  the  Electromotive  Force  existing  at  the  Surface 
of  Reversible  Electrodes.  —  The  potential-difference  which  appears 
when  a  reversible  electrode  is  placed  in  contact  with  a  liquid  may 
easily  be  calculated  according  to  the  procedure  given  by  Nernst.  At 
the  same  time,  the  mathematical  importance  of  the  electrolytic  solu- 
tion pressure  will  be  made  evident. 

Let  us  consider  the  following  isothermal,  reversible,  cyclical  pro- 
cess, noting  first,  however,  that  only  the  pressure  of  the  correspond- 
ing ions  come  into  consideration,  e.g.  in  the  case  of  a  silver  elec- 
trode, only  the  silver  ions  need  be  considered.  Let  F  represent  the 
desired  potential-difference,  and  P  the  osmotic  pressure  of  the  univ- 
alent  ions  corresponding  to  the  metal  of  the  electrode. 

PART  1.  The  quantity  of  electricity  Q  is  passed  from  the  elec- 
trode into  a  solution  of  osmotic  ion-pressure  P,  at  a  potential  F. 
The  quantity  of  work  thereby  obtained  from  the  system  is  given  by 
the  equation 

TFf  =  FQ. 

PART  2.  The  equivalent  of  ions  of  volume  V  which  has  been 
formed  in  solution  is  now  diluted  reversibly  to  the  volume  F+  dV, 
and  the  following  quantity  of  work  is  obtained  :  — 

W"=PdV. 

Quantities  of  work  of  the  second  order  of  magnitude  have  here  been 
neglected. 

PART  3.     Since,  in  the  above  part,  the  volume  has  been  increased 

1  Ztschr.  Elektrochem.,  8,  496  (1902).  See  also  Brunner,  Ztschr.  Elektro- 
chem.,  11,  415  (1905). 


182  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

to  V  4-  d  V,  the  osmotic  pressure  of  the  ions  under  consideration  has 
been  decreased  to  P  —  dP  and  the  potential-difference  at  the  surface 
of  contact  of  this  diluted  solution  and  the  electrode  has  been  in- 
creased to  F  +  dv.  Hence  now  when,  under  these  new  conditions, 
one  equivalent  of  the  ions  is  separated  out  of  solution,  the  quantity 
of  work  consumed  is  as  follows  :  — 


The  process  is  now  complete  and  the  quantities  of  work  involved 
in  the  different  parts  may  be  summarized.  Representing  the  work 
done  by  the  system  by  a  plus,  and  that  done  upon  the  system  by  a 
minus  sign,  then  the  sum  must  be  equal  to  zero,  or  :  — 


Hence  Qcte  =PdV. 

Since,  according  to  Boyle's  law,  at  constant  temperature,— 

0,  andF  =  —  , 


it  follows  that  gdF  =  -  VdP  =  -HT, 


or,  after  integration,     F  =  --  —  -  In  P  +  const. 

Instead  of  the  constant  appearing  in  the  last  equation,  the  logarithm 

n  rri 

of  another  constant  P,  multiplied  by  -  ,  may  be  substituted.    This 
equation  then  becomes 


Q 
When  p  =  P,  F  =  0, 

and  the  constant  P  receives  a  comprehensible  significance  and  is 
known  as  the  electrolytic  solution  pressure. 

If  the  ion  is  not  univalent,  but  polyvalent,  then  the  electrical 
work  VFQ  per  gram-ion  is  involved  where  v  is  the  valency  of  the 
ion.  The  above  equation  then  becomes 

ET,    P 

F  =  -  In  —  • 

VQ         P 

The  quantity  -  is  called  the  "  electrolytic  gas  constant,"  and  its 

Q 
value  is  0.861  x  10  ~4, 

when  the  value  of  F  is  desired  in  volts. 


ELECTROMOTIVE   FORCE  183 

Hence  the  above  equation  may  be  written  as  follows:  — 
F  =  0.861  x  10-'  rlogpyolt3) 

or,  after  multiplying  by  2.3026, 

g=0.0001983rlogPvolt9 

Referring  the  above  equation  to  a  room  temperature  of  18°  £,  then 

T=291°, 
and  the  following  equation  is  obtained, 


This  is  a  fundamental  equation  in  the  theory  of  reversible  cells. 
In  considering  a  cell  composed  of  two  metals  and  two  solutions, 
as,  for  instance,  the  Daniell  cell, 

Zn  —  ZnS04  solution  —  CuS04  solution  —  Cu, 

there  are  four  places  where  potential-differences  are  produced  :  — 

1.  At  the  point  of  contact  between  the  two  metals, 

2.  At  the  point  of  contact  between  the  two  liquids, 

3  and  4.  At  the  points  of  contact  of  the  two  electrodes  with  the 
respective  solutions. 

The  potential-difference  at  the  point  of  contact  between  the  two 
metals  is  so  small  that  it  may  be  usually  left  out  of  account.  This 
is  also  often  true  of  that  existing  between  the  two  solutions.  These 
magnitudes  will  shortly  be  calculated.  Considering  only  the  poten- 
tial-differences at  the  points  of  contact  of  the  electrodes  with  the 
liquids,  the  electromotive  force  of  the  cell  at  18°  is  expressed  by  the 
following  equation  :  — 

0.05771,       P*     0.05771  1/w  P' 

*  =  -^—  losp-  -v~logK 

p  represents  the  electrolytic  solution  pressure  of  the  one  substance, 
the  valence  and  osmotic  pressure  of  whose  ions  are  v  and  P; 
while  pf,  V,  and  P  are  the  corresponding  values  for  the  other  sub- 
stance. The  minus  sign  is  used  because  at  one  electrode  ions  enter 
the  solution,  while  at  the  other  they  pass  from  the  solution;  for 
example,  in  the  Daniell  cell  zinc  ions  are  produced,  and  simultane- 
ously an  equal  number  of  copper  ions  separate  at  the  other  electrode  ; 
for  the  same  number  of  positive  and  negative  ions  must  always 


184  A    TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

be  present  in  the  solution.     The  investigation  of  special  cases  will 
now  be  taken  up. 

CONCENTRATION   CELLS 

1.  Different  Concentrations  of  the  Substances  which  are  Electro- 
motively  Active.  —  a.  A  cell  formed  of  two  differently  concentrated 
amalgams  of  the  same  metal,  for  example  zinc,  in  a  solution  of  one 
of  the  salts  of  the  metal,  as  zinc  sulphate,  possesses,  according  to 
the  previous  considerations,  an  electromotive  force  at  T°  expressed 
by  the  equation,  — 


where  p  and  P'  represent  the  electrolytic  solution  pressure  of  the 
zinc  in  the  concentrated  and  in  the  dilute  amalgam,  respectively,  and 
P  the  concentration  of  the  zinc  ions  in  the  solution.  Since  the 
latter  concentration  is  the  same  throughout  the  solution,  the  above 
equation  may  be  simplified  to 

0.0001983  ™  ,      P 
F=  -  -  -  T  log  -,  volts. 

Dilute  amalgams  may  be  considered  to  be  solutions  in  which  the 
mercury  is  the  solvent  and,  in  the  above  case,  zinc  the  dissolved 
substance.  The  zinc,  like  all  dissolved  substances,  exerts  a  certain 
osmotic  pressure  which,  since  the  amalgams  are  not  of  the  same  con- 
centration, is  different  at  the  two  electrodes.  Since  these  are  pro- 
portional to  the  concentrations,  the  electrolytic  solution  pressures  of 
the  amalgams  may  be  assumed  to  be  proportional  to  the  osmotic 
pressures  of  the  dissolved  zinc.1  From  this 


where  C  and  C±  are  the  concentrations  of  the  zinc  in  the  amalgams. 
That  values  of  F  calculated  in  this  manner  agree  with  those  experi- 

1  This  is  equivalent  to  assuming  that  the  dissolved  substance  is  present  in  the 
mercury  as  atoms,  which  will  be  demonstrated  from  a  consideration  of  concen- 
tration cells  formed  from  gases.  If  it  be  assumed  that  a  compound  is  formed 
between  the  mercury  and  the  substance  dissolved  in  it  of  the  type  JT-Hgz,  then 
another  term  must  be  added  to  the  above  equation.  Since  this  term  is  within 
the  limits  of  experimental  error,  the  question  of  the  formation  of  such  a 
compound  remains  unanswered.  It  must  at  least  be  concluded  from  the 
experiments,  either  that  the  molecules  of  dissolved  substance  are  monatomic, 
or  that  they  are  combined  singly  with  the  solvent,  mercury. 


ELECTROMOTIVE   FORCE  185 

mentally  determined  may  be  seen  from  the  following  results  obtained 
by  G.  Meyer : l  — 

Zinc  Amalgam  and  Zinc  Sulphate  Solution 
t  C  Ci  F  found  F  calculated 


11.6° 

0.003366 

0.00011305 

0.0419  volt 

0.0416  volt 

18.0° 

0.003366 

0.00011305 

0.0433  volt 

0.0425  volt 

12.4° 

0.002280 

0.0000608 

0.0474  volt 

0.0445  volt 

60.0° 

0.002280 

0.0000608 

0.0520  volt 

0.0519  volt 

Cadmium  Amalgam  and  Cadmium  Iodide  Solution 
t  C  Ci  F  found  F  calculated 


16.3° 
60.1° 
13.0° 

0.0017705 
0.0017705 
0.0005937 

0.00005304 
0.00005304 
0.00007035 

0.0433  volt 
0.0562  volt 
0.0260  volt 

0.0440  volt 
0.0507  volt 
0.0262  volt 

Copper  Amalgam  and  Copper  Sulphate  Solution 

t        _  C  __  Ci  _          F  found  _  F  calculated 
17.3°          0.0003874       0.00009587  0.01815  volt        0.0176  volt 

20.8°          0.0004472        0.00016645  0.0124    volt        0.0125  volt 

The  electromotive  force  F  of  such  cells  can  be  calculated  in  a 
second  way,  independent  of  the  idea  of  electrolytic  solution  pressure. 
The  action  of  the  cell  consists  in  zinc  passing  from  the  more  con- 
centrated amalgam  into  the  solution,  and  at  the  same  time  from  the 
solution  into  the  weaker  amalgam.  As  a  result  of  the  whole  action, 
zinc  is  transferred  from  the  concentrated  to  the  dilute  amalgam,  or, 
in  other  words,  zinc  at  an  osmotic  pressure  P,  or  the  proportional 
concentration  C,  changes  to  the  osmotic  pressure  Ply  or  the  concen- 
tration Ci.  The  maximum  amount  of  work  thereby  obtainable 
osmotically  is 


for  a  gram-atom,  when  the  metal  is  assumed  to  be  present  in  the 
mercury  in  the  form  of  atoms. 

The  value  of  the  work  obtained  electrically  from  the  same  process 
is  2  x  96540  x  F,  and  since  the  two  maximum  quantities  of  work 
must  be  equal, 


1  Ztschr.  phys.   Chem.,  7,  447  (1891),  and  Ostwald,  Attgem.  Chem.,  II,  1, 
861. 


186  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

0.0001983  „        C 
or  F  =  --  -  --  T  log^  volts. 

*»  Oj 

This  is  the  same  formula  obtained  by  the  previous  method,  and  will 
also  be  used  later  in  the  calculation  of  F. 

It  was  assumed  that  the  metal  is  present  in  the  mercury  in  the 
atomic  state,  and  since  the  experimentally  determined  values  of  F 
agree  with  those  calculated,  this  assumption  may  be  considered 
justified. 

If  the  metals  had  dissolved  in  the  mercury  in  complexes  of  two 
atoms  each,  the  work  obtainable  osmotically,  through  the  trans- 
ference of  the  same  amount  of  metal  as  before,  would  have  been 

C1 


because  the  number  of  separate  particles  to  be  transferred  is  only 
half  as  great.  The  work  obtainable  depends  upon  their  number,  but 
not  upon  their  weight.  The  corresponding  electrical  energy  would  be 

2  x  96540  x  F' 


therefore  2  x  96540  x  F'  =  |  Jjjg  logg, 


,     1      0.0001983  ,      C      I 
and  F'  =  -.        _-log-=-F; 

or  in  such  a  case  the  electromotive  force  of  the  cell  would  be  only 
half  as  great  as  is  actually  found.  The  monatomic  character  of  the 
metal  molecules  in  mercury  solutions  has  also  been  proved  from 
measurements  of  the  vapor-pressure  lowering. 

As  shown  by  the  equation,  F  depends  only  upon  the  relation 
between  the  concentrations  and  upon  the  valence  of  the  metal,  and 
is  in  other  respects  independent  of  the  nature  of  the  metal. 

The  amalgams  have  been  considered  simply  as  differently  concen- 
trated zinc  electrodes;  it  might  be  asked  if  the  mercury  in  them 
does  not  also  play  the  part  of  an  electrode,  and  its  electrolytic  solu- 
tion pressure  come  into  consideration.  In  order  to  dispose  of  this 
question  at  once,  it  may  be  stated  that,  in  the  case  of  electrodes 
composed  of  two  or  more  metals,  three  cases  are  recognized.1 

CASE  1.  If  the  metals  form  a  mechanical  mixture,  the  potential  will 
be  that  of  the  least  noble  metal.  Such  a  mixture  of  metallic  zinc 

i  Herschkowitz,  Ztschr.  phys.  Chem.,  27,  123  (1898)  ;  Ogg,  Ztschr.  phys. 
Chem.,  27,  285  (1898)  ;  Haber,  Ztschr.  Elektrochem.,  8,  541  (1902)  ;  Reinders, 
Ztschr.  phys.  Chem.,  42,  225  (1902). 


ELECTROMOTIVE   FORCE  187 

and  metallic  cadmium,  for  example,  when  used  as  the  negative  elec- 
trode of  a  cell  containing  acid,  sends  practically  only  zinc  ions  into 
the  solution.  The  electromotive  force  is,  therefore,  at  first  that  of 
pure  zinc. 

If  zinc  ions  be  added  to  the  solution,  but  little  effect  is  produced. 
Only  a  small  quantity  of  cadmium  dissolves.  On  the  other  hand,  if 
cadmium  ions  be  added  to  the  solution,  a  considerable  secondary 
reaction  results.  This  proceeds  until  such  a  number  of  cadmium 
ions  have  been  deposited  and  replaced  by  zinc  ions  as  will  make  the 
potential-difference  between  the  zinc  and  the  zinc  ions  equal  to  that 
between  the  cadmium  and  the  cadmium  ions.  When  this  has  occurred, 
again  practically  only  pure  zinc  goes  into  solution. 

The  above-mentioned  equality  of  the  potential-differences  between 
the  metals  and  the  solution  is,  under  all  circumstances,  spontaneously 
established,  i.e.  a  local  action  takes  place  until  it  is  established.  Since 
the  individual  potential-differences  depend  upon  the  relation  between 
the  electrolytic  solution  pressure  and  the  osmotic  pressure  of  the 
corresponding  ions,  evidently  in  the  case  of  equi-valent  metals,  the 
osmotic  pressures  of  the  corresponding  ions  must  be  related  to  each 
other  as  the  solution  pressures,  in  order  that  equality  of  potential- 
difference  may  be  attained.  In  the  case  of  great  differences  in  the 
solution  pressures,  as,  for  example,  between  zinc  and  cadmium, 
the  concentration  of  the  cadmium  ions  must  be  extremely  small  as 
compared  with  that  of  the  zinc  ions.  Since,  because  of  the  extreme 
smallness  of  the  former  concentration,  it  is  greatly  changed  by  the 
addition  of  new  quantities  of  cadmium  ions,  while  the  latter  concen- 
tration is  but  slightly  changed  by  the  addition  of  a  far  greater 
quantity  of  zinc  ions,  it  is  evident  that,  if  the  potential-differences 
must  remain  the  same,  practically  only  zinc  ions  will  go  into 
solution. 

In  the  case  of  a  mixture  of  two  equi-valent  metals  which  possess 
the  same  electrolytic  solution  pressure,  equilibrium  is  only  established 
when  the  two  corresponding  ion  concentrations  are  equal,  i.e.  when 
the  two  metals  dissolve  to  the  same  extent  in  the  solution. 

CASE  2.N  If  the  metals  form  a  solution  (amalgam  or  alloy),  the 
latter  is  always  more  noble  than  the  least  noble  component,  and, 
further,  this  is  true  to  a  greater  extent,  the  greater  the  loss  in  free 
energy  accompanying  the  formation  of  the  alloy.  It  may  even 
happen  that  the  metallic  solution  is  more  noble  than  the  noblest 
component. 

The  solution  or  dissolving  of  such  alloys  takes  place  in  a  manner 
analogous  to  that  already  outlined.  In  all  cases,  the  potential- 


188  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

differences  between  the  alloy  of  the  least  noble  metal  and  the  ions 
of  this  metal,  and  between  the  alloy  of  the  more  noble  metal  and 
the  ions  of  this  metal,  must  be  equal  to  each  other.  It  is  to  be 
noted,  however,  that  this  potential-difference  is  not  the  same  as  that 
which  would  exist  between  the  pure  metals  and  the  same  solution, 
and,  further,  that  because  of  the  dependence  of  the  electrolytic  solu- 
tion pressure  upon  the  concentration  of  the  metal  in  the  alloy,  it 
changes  with  the  composition  of  the  alloy.  If  the  solution  pres- 
sures of  the  two  alloyed  metals  differ  very  greatly,  as  is  usually  the 
case,  then  the  least  noble  metal  is  practically  the  only  one  which 
dissolves  in  the  solution. 

CASE  3.  If,  finally,  the  metals  form  a  chemical  compound  with 
each  other,  and  if  this  compound  can  exist  as  such  in  the  solution, 
which  contains  a  definite  quantity  of  the  metal  ions  corresponding 
to  the  constituent  metal  of  the  compound,  as,  for  example,  copper 
and  zinc  ions  in  the  case  of  a  zinc-copper  compound,  then  this  com- 
pound possesses  its  own  electrolytic  solution  pressure.  From  this  it 
must  be  concluded  that  during  the  solution  of  the  electrode,  ions  of 
the  same  composition  as  the  electrode  are  sent  into  the  solution, 
where  they  eventually  are  dissociated  to  a  large  extent  into  the 
individual  components.  In  this  case,  the  potential-difference  is 
dependent  upon  the  product  of  the  concentrations  of  these  individual 
ions. 

To  avoid  errors  in  the  interpretation  of  the  phenomena,  it  must  be 
borne  in  mind  that  only  the  composition  of  the  layer  of  the  electrode 
which  is  in  direct  contact  with  the  electrolyte  is  of  influence  upon 
the  electrolytic  solution  process.  The  composition  of  this  layer,  in 
the  case  of  a  solid  alloy,  may  change  by  the  gradual  solution  of  the 
less  noble  metal  alone.  Since  an  appreciable  diffusion  cannot  take 
place,  the  more  noble  metal  remains  alone  upon  the  surface  of  the 
electrode.  Hence  it  is  that  such  an  alloy  exhibits,  after  a  time,  the 
potential  and  other  properties  of  the  more  noble  metal. 

Advantage  is  taken  of  the  fact  that  the  least  noble  metal  dissolves 
first,  in  the  preparation  of  pure  metal  surfaces.  When  a  metal  con- 
taining a  quantity  of  a  less  noble  metal  is  placed  in  a  solution  of 
one  of  its  salts,  the  latter  metal  goes  into  solution  accompanied  by 
the  deposition  of  some  of  the  former  metal  from  the  solution.  In 
this  manner,  it  is  possible  to  free  the  entire  mass  of  mercury  from 
the  less  noble  metals  dissolved  in  it. 

The  same  principles  play  a  very  important  part  in  the  commercial 
purification  of  metals.  For  example,  copper  is  purified  by  placing 
the  impure  copper  plate,  as  an  anode,  in  an  acid  solution  of  copper 


ELECTROMOTIVE  FORCE  189 

sulfate  of  a  certain  concentration,  near  a  suitable  cathode,  upon 
which  the  pure  copper  is  to  be  deposited.  When,  now,  an  electric 
current  is  passed  through  the  cell  thus  formed,  the  less  noble 
metals  contained  in  the  impure  copper  plate  dissolve  first,  but  do 
not,  as  will  be  shown  in  the  chapter  on  electrolysis  and  polarization, 
deposit  upon  the  cathode.  Thereafter  the  copper  goes  into  solution. 
When  the  impure  anode  plate  is  nearly  consumed,  what  remains  of  it 
is  composed  of  copper,  and  the  more  noble  metals,  silver  and  gold. 
The  latter  metals  have,  then,  been  concentrated  partly  in  the  remains 
of  the  anode  and  partly  in  the  anode  mud  which  falls  from  the  anode 
during  the  electrolysis.  Thus  not  only  is  the  copper  purified  by 
this  process,  but  also  the  more  noble  metals  are  so  concentrated  that 
they  may  easily  be  obtained  in  the  pure  state. 

The  important  practical  question  as  to  whether  iron  is  better  pro- 
tected by  a  coating  of  a  more,  or  of  a  less,  noble  metal,  e.g.  by  a  coat- 
ing of  copper  or  of  zinc,  can  now  be  considered.  As  long  as  only 
impenetrable  coatings  are  to  be  considered,  that  one  would  naturally 
be  chosen  which  best  resists  the  action  of  the  atmosphere.  Of  the 
two  metals  just  mentioned,  copper  would  be  preferred.  On  the 
other  hand,  if  coatings  which  are  penetrable,  as  are  all  coatings  in 
practice,  are  to  be  considered,  then,  since  moisture  is  always  present, 
at  the  points  of  penetration  there  will  be  a  mixture  of  two  metals 
in  contact  with  a  liquid.  According  to  the  principles  already 
studied,  at  these  points  the  less  noble  of  the  two  metals  will  be  acted 
on  by  the  moisture.  Hence  if  the  iron  is  covered  with  zinc,  as  long 
as  the  zinc  remains  it  will  dissolve  and  protect  the  more  noble  metal, 
iron,  while  if  the  iron  be  covered  with  copper,  it  is  not  at  all  pro- 
tected thereby,  but,  on  the  other  hand,  its  corrosion  is  accelerated. 

From  the  same  point  of  view,  the  fact  that  aluminium  cannot  be 
durably  soldered  may  be  explained.  Since  only  the  more  noble 
metals  are  suitable  for  soldering,  in  the  case  of  such  a  metal  as 
aluminium  a  galvanic  cell  is  formed  at  the  soldered  points  which, 
when  in  action,  causes  the  aluminium  to  go  over  into  the  ionic  state. 
The  aluminium  thus  dissolved  finally  becomes  oxidized  to  aluminium 
oxide,  forming  the  observed  fungus-like  growth. 

b.   The  combination, 

Hg  —  Hg  (-ous)  salt  solution  —  Amalgam  of  a  noble  metal, 

can  also  be  classed  as  a  concentration  cell.  It  is  evident  from  the 
discussion  in  the  previous  section  that  in  this  cell  the  mercury  is 
present  in  different  concentrations  at  the  two  electrodes.  Naturally 
only  those  metals  may  be  used  to  dilute  the  mercury  whose  solution 


190 


A   TEXT-BOOK   OF   ELECTRO-CHEMISTRY 


pressure  is  less  than  that  of  the  mercury,  as,  for  example,  the  so- 
called  noble  metals,  gold  and  platinum.  A  mercurous  salt  must  be 
used  as  the  electrolyte.  Murcuric  salts  are  immediately  reduced  to 
the  mercurous  state  when  brought  into  contact  with  metallic  mer- 
cury, according  to  the  equation  — 

Hg'  *+Hg  =  2Hg. 

The  electromotive  force  of  this  mercury  concentration  cell  may  be 
easily  calculated,  as  was  that  of  the  previously  described  cell,  either 
with  or  without  the  use  of  the  idea  of  electrolytic  solution  pressure. 
It  will  be  sufficient  to  apply  the  shorter  method,  since  the  electromo- 
tive force  of  such  a  cell  has  not  yet  been  experimentally  determined. 
During  the  action  of  the  cell,  mercury  dissolves  from  the  pure 
mercury  electrode,  where  the  solution  pressure  is  greater,  and  is 
precipitated  upon  the  amalgam  electrode.  The  maximum  work 
available  osmotically  will  now  be  calculated  and  placed  equal  to  the 
maximum  available  electrical  work. 

Let  us  consider  a  system  such  as  is  shown  in  Figure  42,  in  which 
the  pure  solvent,  mercury,  is  separated  from  the  solution  of  a  metal 

in  mercury,  the  amalgam,  by  a 
movable  semipermeable  piston. 
Let  P  represent  the  osmotic  pres- 
sure of  the  solution,  and  V  the 
volume  of  it  which  contains  one 
mol  of  the  dissolved  metal.  Now 
let  the  semipermeable  piston  be 
moved  downward  under  the  con- 
stant pressure  p,  from  the  point  a 
to  the  point  6,  whereby  the  volume 
Fof  the  pure  solvent  enters  the 
solution.  If,  for  example,  this 
volume  is  one  cubic  meter,  then 
one  cubic  meter  of  the  solvent 
passes  through  the  piston  into  the 

solution,  and  the  piston  is  moved  through  the  volume  of  one  cubic 
meter  at  the  constant  pressure  p.  Finally,  let  the  volume  of  the 
solution  be  so  great  that  the  introduction  into  it  of  the  volume  V 
of  the  solvent  causes  no  appreciable  change  in  its  concentration. 
Since  V  is  the  volume  of  the  solution  containing  one  mol  of  the  dis- 
solved substance,  the  maximum  quantity  of  work  which  can  thus  be 
obtained  is  as  follows :  — 


LA  large 

I 
Volume 

of 

a                                  < 

ion  ofany 

Metal  in  Mercury 

P                                    ' 

===---=•--=--  =  — 


Mercuuj 


FIG.  42 


ELECTROMOTIVE   FORCE 


191 


But 

and  consequently 


PV=RT, 
W08  =  RT, 


where  W^  represents  the  maximum  quantity  of  work  obtainable 
osmotically.  In  order  to  obtain  the  equivalent  electrical  energy  of 
work,  the  number  of  equivalents  of  mercury  (n)  contained  in  the 
volume  V  must  be  dissolved  at  one  electrode  and  deposited  at 
the  other  electrically.  The  electrical  work  is  then  given  by  the 
equation, 

We  =  WFQ  ; 

therefore  WFQ  =  RT, 

RT 


or 


F  = 


The  values  of  Ry  T,  and  Q  are  known,  and  that  of  n,  the  number  of 
equivalents  of  mercury  containing  one  mol  of  dissolved  metal  in  the 
amalgam,  may  be  found.  Hence  the  value  of  F  is  easily  calculated. 

This  method  serves  also  for  determining  the  molecular  weight  of 
the  noble  metals  dissolved  in  the  mercury ;  n  is  the  number  of  mols 
of  mercury  containing  one  mol  of  the  dissolved  metal.  By  measur- 
ing F,  n  is  obtained,  and  from  the  known  concentration  of  the  amal- 
gam, the  weight  of  the  dissolved  substance  in  n,  which  represents 
the  molecular  weight,  is  calculable. 

c.   A  second  mercury  concentration  cell  is  the  following :  — 

Mercury  (p  >  pat)  —  Mercurous  salt  sol.  —  Mercury  (p  =pat), 

where  p  and  pat  represent  the 
pressure  upon  the  mercury  and 
the  atmospheric  pressure  respec- 
tively. [It  is  shown  in  Figure 
43.]  In  such  a  cell  mercury  passes 
from  the  former  electrode  through 
the  electrolyte  to  the  latter.  Des 
Coudres1  arranged  this  cell  as 
follows :  A  column  of  mercury  of 
height  d  formed  one  electrode; 
the  lower  end  of  the  tube  con- 
taining it,  closed  by  means  of 
parchment  paper,  was  placed  in 
a  salt  solution.  The  paper  was 
impervious  to  the  mercury  as 
such,  but  allowed  the  passage  of 

it  in  the  form  of  ions.     The  surface  of  the  second  mercury  electrode 
1  Wied.  Ann.,  46,  292  (1892). 


192  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

was  at  the  level  of  the  parchment  membrane.  The  height  of  the 
mercury  column  decreases  by  a  definite  amount  when  a  mol  of  mer- 
cury passes  from  the  electrode  under  pressure  p  to  the  other  under 
the  pressure  pat.  The  maximum  work  thus  obtainable  may  be  cal- 
culated, and  placed  equal  to  the  electrical  energy  involved.  The 
work  necessary  for  the  transference  of  the  ions  through  the  solution 
may  be  left  out  of  account.  If  200  grams  thus  leave  the  column  of 
mercury,  which  is  of  great  height  d,  the  effect  is  the  same  as  though 
200  grams  of  mercury  had  fallen  the  distance  d.  The  maximum 
available  mechanical  energy  is  200  d  gram-centimeters,  where  d  is 
expressed  in  centimeters.  Therefore,  since,  according  to  page  17, 
gram-centimeter  units  must  be  divided  by  10,198  in  order  to  obtain 
electrical  units, 

FQ-   2°°<* 

-10198' 

and  the  electromotive  force  has  the  value  given  in  the  following 
equation  :  — 


F==  _  volts. 

96540x10198 

In  the  following  table,  experimentally  determined  values  are 
compared  with  those  calculated  with  the  aid  of  the  above  equa- 
tion :  — 


PRESSURE  IN  CM. 

F   CALCULATED             f,- 

T  FOUND 

36 
46 
113 

7.2  x  10-6  volts 
9.  3xlO-6  volts 
23  x  10~6  volts 

7.4  x  10-6  volts 
10.  5xlO-6  volts 
21  x  lO-6  volts 

Considering  the  difficulty  of  accurately  measuring  these  small 
values,  the  agreement  must  be  considered  satisfactory. 

In  this  connection,  it  is  of  interest  to  inquire  the  value  of  the 
electromotive  force  which  would  be  obtained  if  the  above  experi- 
ment be  so  changed  that  mercury  columns  of  the  same  height  but 
situated  at  different  levels  in  the  solution  are  used  as  electrodes. 
If  the  difference  between  the  levels  of  the  two  electrodes  is  equal 
to  d  centimeters,  will  the  electromotive  force  be  the  same  as  in 
the  former  experiment  ?  As  before,  by  the  passage  of  one  mol  of 
mercury  from  the  higher  to  the  lower  electrode,  the  following 
maximum  quantity  of  work  can  be  obtained :  — 

W  =  200  d  gram-centimeters. 


ELECTROMOTIVE   FORCE  193 

Nevertheless,  in  answer  to  this  question,  it  may  be  stated  that  the 
electromotive  force  of  the  latter  must  always  be  less  than  that  of 
the  former  cell,  and  that,  moreover,  under  certain  circumstances  the 
direction  of  the  current  may  even  be  reversed.  This  is  due  to  the 
fact  that  the  migration  downward  of  the  mercury  ions  necessitates 
the  corresponding  migration  upward  of  the  negative  ions,  which  latter 
requires  the  expenditure  of  work.  As  long  as  the  mass  of  negative 
ions  migrated  upward  is  less  than  that  of  the  positive  ions  migrated 
downward,  an  electric  current  flows  through  the  solution  from  the 
lower  electrode.  When,  however,  the  mass  of  the  negative  is  the 
greater,  work  may  be  obtained  through  the  migration  downward  of 
the  negative  ions  and  the  corresponding  migration  upward  of  the 
positive  ions.  In  this  case  the  direction  of  the  electric  current  is 
reversed,  i.e.  the  current  flows  through  the  solution  from  the 
lower  to  the  higher  electrode.  It  is  evident  that  here  the  trans- 
ference number,  as  well  as  the  mass,  of  an  ion  plays  an  important 
part,  and,  moreover,  that  a  deficiency  in  mass  of  a  given  ion  may  be 
compensated  by  a  greater  speed  of  migration. 

Eecent  investigations  carried  out  by  K.  K.  Kamsay1  on  the  influ- 
ence of  gravity  upon  electrolytic  phenomena  have  confirmed  the 
above  conclusions.  For  example,  in  the  case  of  a  ten  per  cent  solu- 
tion of  zinc  sulfate,  the  current  flows  through  the  solution  from  the 
lower  to  the  upper  zinc  electrode.  This  would  be  expected,  from  the 
fact  that  while  32.5  grams  of  zinc  are  migrated  upward  in  a  given 
time,  57.7  grams  of  sulfate  ions  are  migrated  downward. 

After  this  experience,  the  fact  that  when  two  pieces  of  the  same 
metal,  in  which  respectively  the  metal  exists  in  different  modifica- 
tions, or  in  which  it  possesses  any  difference  in  physical  structure  or 
quality,  are  dipped  into  a  solution  and  then  brought  into  contact,  an 
electric  current  is  produced,  is  no  longer  particularly  wonderful. 
Thus  iron  which  has  been  subjected  to  tension  or  pressure  possesses 
a  greater  electrolytic  solution  pressure  than  ordinary  iron.  The 
recognition  of  this  fact  is  of  importance  in  so  far  as  it  furnishes 
an  explanation  for  the  very  active  corrosion  at  certain  places  on  iron 
cables  and  boiler  plates.  It  may  be  stated  in  general  that  iron  which 
has  been  subjected  to  an  uneven  strain,  or  which  has  not  been  uni- 
formly treated,  corrodes  more  readily  than  does  iron  which  has  been 
treated  uniformly ;  and,  further,  that  highly  polished  corrodes  less 
readily  than  unpolished  or  poorly  polished  iron.2 

Since  the  transformation  of  an  unstable  form,  or  a  form  which  is 

1  Ztschr.  phys.  Chem.,  41,  121  (1902). 

2  Jahrbuch  der  Elektrochemie,  8,  224  (1902). 


194 


A   TEXT-BOOK  OF   ELECTRO-CHEMISTRY 


produced  by  the  action  of  an  external  force,  into  the  form  which  is 
stable  under  ordinary  conditions,  is  a  process  which  takes  place 
spontaneously,  and  which  is  capable  of  producing  work,  the  electric 
current  always  flows  in  such  a  direction  that  the  unstable  may  pass 
over  into  the  stable  form. 

</.  Finally,  concentration  cells  may  be  produced  from  gases,  or 
aqueous  solutions  of  different  concentrations,  as  ion-producing  sub- 
stance. At  the  first  glance  it  may  seem  im- 
probable that  gases  or  liquids,  which  pos- 
sess no  metallic  conductance,  can  serve  as 
electrodes.  [Nevertheless,  by  means  of  a 
special  arrangement,  such  as  is  represented 
in  Figure  44,  this  end  is  easily  attained.]  A 
platinized  platinum  electrode  (Pt)  is  passed 
into  a  tube  which  is  afterward  closed,  so 
that  its  lower  end  extends  into  a  liquid. 
The  tube  is  so  filled  with  the  gas  under  con- 
sideration that  the  platinum  plate  is  for  the 
greater  part  in  the  gas,  the  remaining  por- 
tion being  in  the  liquid.  The  platinized 
platinum  absorbs  a  certain  quantity  of  the 
gas,  and  may  then  be  considered  as  a  gas 
electrode.  The  only  other  part  the  platinum 
plays  in  these  cells  is  that  of  conductor  of 
the  electricity.  Because  of  its  power  of 
dissolving  the  gases  the  platinum  permits 
the  change  from  the  gaseous  to  the  ionic 
state,  and  the  reverse,  without  resistance.  Such  an  electrode,  e.g. 
one  of  hydrogen,  belongs  to  the  reversible  class,  as  has  been  experi- 
mentally shown  by  Le  Blanc.1  The  quantity  of  work  developed  by 
the  passage  of  a  certain  quantity  of  gas  into  the  ionic  condition  is 
exactly  the  quantity  necessary  and  sufficient  to  produce  the  reverse 
action.  Since  this  is  true,  the  material  of  the  metallic  electrode  can 
have  no  effect  upon  the  electromotive  force,  and,  in  fact,  equal  values 
have  been  obtained  with  platinum  and  palladium  electrodes. 

By  means  of  such  platinized  platinum  electrodes,  reversible  hydro- 
gen, oxygen,  chlorine,  bromine,  and  iodine  electrodes  may  be  pre- 
pared. By  arranging  a  reversible  cell  of  two  such  electrodes,  using 
as  ion-producing  material  the  same  substance  for  each,  but  in  differ- 
ent concentrations,  a  concentration  cell  entirely  analogous  to  that  of 
the  amalgam  results.  The  electrolyte  to  be  used  must  evidently  be 

i  Ztschr.  Phys.  Chem.,  12,  333  (1893). 


FIG.  44 


ELECTROMOTIVE   FORCE  195 

one  containing  the  same  ions  as  the  gas  produces.  If,  for  example, 
hydrogen  be  the  gas,  an  acid  must  be  used  ;  if  oxygen,  the  corre- 
sponding ions  of  which  are  OH  (or  0  ions),  a  solution  of  a  base 
must  form  the  electrolyte.  This  kind  of  a  cell  is  independent  of  the 
nature  of  the  electrolyte,  except  for  the  above  consideration  defining 
one  of  the  ions. 

In  the  calculation  of  the  electromotive  force  of  a  gas  cell,  for 
example  one  consisting  of  two  hydrogen  electrodes  under  the  pres- 
sures p  and  pl)  the  process  is  the  same  as  with  the  amalgam  cell,  ex- 
cept that  it  must  be  borne  in  mind  that  the  hydrogen  molecule 
contains  two  atoms.  In  the  reversible  change  of  one  mol  of  hydro- 
gen from  the  pressure  p  to  plf  the  maximum  work  is  represented  by 


Pi 

The  corresponding  energy,  when  the  process  is  considered  as  an 
electrical  one,  is  2FQ  because  one  molecule  of  hydrogen  produces 
two  univalent  ions  ;  therefore 

RT,   p 

F  =  -__  ln-£-. 
2q     p, 

The  factor  2  occurs  here  in  the  denominator,  even  though  the  equa- 
tion applies  in  this  case  to  univalent  ions. 

If  the  calculation  be  made  in  accordance  with  the  osmotic  process, 
using  solution  pressures  as  on  page  184,  the  equation  is 


,    p 

-  In  —  , 
Q         V 

p  and  P!  being  the  solution  pressures  of  the  gas  corresponding  to  the 
pressures  p  and  pt  respectively.  Evidently  the  two  must  be  equal, 

RT,    p       RT,     p 

or  -TT—  In  —  =  -  In  —  , 

2Q       p,        Q         P/ 

and  jhn^  =  lnl; 

2      Pi  V 

therefore  —  =  —  5  . 

Pi      PI 

That  is,  the  squares  of  the  solution  pressures  are  in  the  same  ratio 
as  the  corresponding  gas  pressures.  This  result  is  not  difficult  to 
understand.  It  may  be  recalled  that  P  and  pl  represent  osmotic 
pressures  (page  177).  If  the  osmotic  pressure  P  exists  in  a  solution 


196  A    TEXT-BOOK  OF   ELECTRO-CHEMISTRY 

at  the  one  gas  electrode  whose  gas  pressure  is  p,  while  at  the  other 
the  osmotic  pressure  is  P!  and  the  gas  pressure  plf  there  is  no  poten- 
tial-difference at  the  electrodes.  There  is  a  condition  of  equilibrium 
between  the  gas  molecules  H2  and  the  corresponding  ions  H'.  When 
such  a  condition  exists  that  the  undissociated  portion  H2  and  the  dis- 
sociated portions  H'-f  H*  are  in  equilibrium,  the  concentration  of  the 
undissociated  portion,  divided  by  the  product  of  the  concentrations 
of  the  dissociated  portions,  is  a  constant. 


Moreover,  the  gas  and  osmotic  pressures  are  proportional  to  the  con- 
centration, hence 


and  also  "=  K', 

pi 

»  p2 

therefore  ^  =  —5-* 

Pi       fi 

Recently  quantitative  measurements  of  the  electromotive  force  of 
such  cells  have  been  made,  the  results  of  which  are  in  agreement 
with  the  predictions.  A  somewhat  complicated  case  will  now  be 
considered. 

A  hydrogen  sulfide  concentration  cell  has  been  investigated  by 
Bernfeld.1  Hydrogen  sulfide  dissociates  according  to  the  equation, 


and  to  an  extremely  slight  extent  according  to  the  equation, 

>2H'  +  S", 


and  always  in  such  a  manner  that  an  equal  number  of  positive  and 
negative  ions  are  formed.  Hence  it  is  evident  that  this  gas  would 
produce  no  current  in  such  an  arrangement  as  is  used  for  the  hydrogen 
concentration  cell.  However,  by  means  of  an  artifice,  a  reversible 
hydrogen  sulfide  concentration  cell  can  be  made. 

The  following  reaction  takes  place  between  hydrogen  sulfide  and 
lead  sulfide  :  — 


Ztschr.  phys.  Chem.,  25,  46  (1898). 


ELECTROMOTIVE   FORCE 


197 


If  now  two  lead  electrodes  which  have  been  covered  with  a  thin 
layer  of  lead  sulfide  be  partially  submerged  in  a  solution  of  sodium 
sulfhydrate  of  a  definite  concentration  and  partially  enveloped  by 
hydrogen  sulfide  gas  of  different  concentrations,  two  systems  are  ob- 
tained which,  with  the  exception  of  the  concentrations  of  the  hydro- 
gen sulfide  gas,  are  identical.  Upon  connecting  the  two  electrodes 
thus  formed  by  means  of  a  wire,  an  electric  current  is  obtained.  As 
the  current  passes,  the  hydrogen  sulfide  gas  under  the  greater  pres- 
sure enters  the  following  reaction :  — 

H2S  +  PbS->Pb+2HS'; 

while  at  the  other  electrode,  the  following  reaction  occurs :  — 
2  HS'  +  Pb  ->  PbS  +  H2S. 

Since  in  this  cell  negative  ions  form  and  disappear,  the  direction  of 
the  current  is  the  reverse  of  that  of  the  hydrogen  cell.  The  values 
of  the  electromotive  force  of  the  two  cells  are,  however,  the  same 
when  the  respective  gases  are  maintained  under  the  same  pressures. 
That  of  the  hydrogen  sulfide  cell  is  as  follows :  — 

_F  =  — 

2Q 

It  is  evident  that  the  nature  of  metal  sulfide  forming  the  elec- 
trodes does  not  come  into  consideration,  and  it  would  be  expected, 
therefore,  that  the  same  value  of  the  electromotive  force  would  be 
obtained  if,  instead  of  the  lead-lead  sulfide,  silver-silver  sulfide  or 
bismuth-bismuth  sulfide  electrodes  were  used.  This  conclusion  is 
well  confirmed  by  the  results  contained  in  the  following  table  :  — 


ELECTRODES         = 

Pb  -  PbS 

Ag-AgS 

Bi  -  Bi28, 

PH2S 

37.50    37.61    37.44 

35.1    34.6 

37.50    37.60    37.50 

P'H* 

15.56     6.26      12.91 

4.2       5.2 

1.71       4.27       2.92 

Millivolts  calc.     = 
Millivolts  found  = 

-11.0  -22.4  -13.3 
-  8.9  -21.1  -10.9 

-26.6  -23.7 
-25.0  -21.4 

-38.6  -27.2  -34.3 
-36.8  -25.8  -32.7 

The  consideration  of  a  second  kind  of  concentration  cell  will  now 
be  taken  up. 
2.   Different  Concentrations  of  the  Ions. — (a)  The  combination, 

Ag  —  AgN03  sol.,  dilute  —  AgN03  sol.,  concentrated  —  Ag, 
may  be  considered  as  a  type  of  these  cells.    In  such  a  cell,  where 


198  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

the  electrode  furnishes  positive  ions,  the  current  always  flows 
through  the  cell  (not  through  the  external  circuit)  from  the  dilute 
to  the  concentrated  solution.  Silver  is  dissolved  into  the  dilute 
solution  and  precipitated  from  the  other,  this  process  continuing 
until  the  two  solutions  become  of  the  same  concentration.  That  the 
silver  ions  must  precipitate  from  the  more  concentrated  solution  is 
evident  when  it  is  remembered  that  the  osmotic  pressure  here  di- 
rected against  the  solution  pressure  is  greater  than  in  the  dilute 
solution.  If  the  electrodes  furnish  negative  ions,  then  the  current 
flows  through  the  cell  from  the  solution  most  concentrated,  to  that 
most  dilute,  in  respect  to  the  negative  ions.  It  will  be  remembered 
that  by  current  direction  is  meant  the  direction  in  which  the  posi- 
tive ions  migrate. 

Leaving  out  of  account  for  the  present  the  potential-difference 
which  exists  at  the  point  of  contact  between  the  two  solutions,  the 
electromotive  force  of  such  a  cell  is  given  by  the  equation, 


where  p  is  the  electrolytic  solution-pressure  of  silver,  and  P  and  Pl 
are  the  osmotic  pressures  of  the  silver  ions  in  the  concentrated  and 
the  dilute  solution,  respectively.  Since  the  solution  pressures  are 
the  same,  the  formula  may  be  simplified  to 


This  expresses  the  fact  that  the  electromotive  force  of  such  a 
cell  is  dependent  only  upon  the  relation  between  the  osmotic  pressures 
and  upon  the  valence  of  the  metal  ions,  and  is  independent  both  of 
the  nature  of  the  metal  and  of  the  negative  ions  of  the  electrolyte. 

The  electromotive  force  may  also  be  ascertained  by  the  second 
method,  through  calculating  the  maximum  of  energy  represented  by 
the  osmotic  change  when  one  ion  equivalent  of  silver  migrates  from 
one  electrode  to  the  other.  For  this  purpose  the  conditions  of  the 
cell  before  and  after  the  electrolysis  are  compared. 

If  one  ion  equivalent  of  silver  dissolves  in  the  dilute  solution, 
the  silver  concentration  is  increased  by  one  ion  equivalent,  but  at 
the  same  time  some  silver  also  passes  from  the  dilute  to  the  concen- 
trated solution.  If  (1  —  nay  be  the  transference  number  of  the 
silver,  1  —  na  ion  equivalents  leave  the  dilute  solution,  and  the  actual 

1  See  page  70. 


ELECTROMOTIVE   FORCE  199 

increase  in  the  concentration  of  the  latter  when  one  ion  equivalent 
dissolves  is  na  ion  equivalents.  The  more  concentrated  solution 
must  evidently  have  its  concentration  reduced  by  this  amount.  A 
migration  of  N03  ions  also  takes  place.  If  na  represent  the  share 
of  transport  for  this  ion,  then  naN03  ion  equivalents  pass  from  the 
concentrated  to  the  dilute  solution,  since  the  motion  is  in  the  direc- 
tion opposite  to  that  of  the  silver  ions.  Consequently  1  —  na  ion 
equivalents  of  silver  and  the  same  number  of  ion  equivalents  of  N03 
move  from  the  concentrated  solution  to  the  dilute  during  the  passage 
of  96,540  coulombs,  i.e.  from  osmotic  pressure  P  to  Px.  The  rela- 

tion of  the  osmotic  pressures  of  the  anions  as  well  as  of  the  cations 

•p 

is  —  .    The  work  is  expressed  by  the  equation, 
*i 


W=2naRTln—  , 


and 


On  comparing  this  equation  for  the  electromotive  force  in  the 
case  of  univalent  metals  with  that  obtained  above,  it  is  seen  that 
when  na  =  £,  i.e.  when  the  two  ions  have  equal  velocities  of  migra- 
tion, the  equations  become  identical.  When  this  is  not  the  case,  a 
potential-difference  exists  (see  later)  at  the  point  of  contact  between 
the  solutions,  and  this  requires  the  application  of  a  correction  to  the 
previous  equation  ;  consequently  the  formula  just  derived  is  more 
general  in  its  application.  It  will  be  assumed  for  the  present  that 
w«  =  i- 

The  following  formula  is  the  most  general  one  :  — 


or  F==«« 

(VQ) 

Here  VQ  is  the  quantity  of  electricity  which  must  flow  through 
the  cell  in  order  to  cause  na  mols  of  the  electrolyte  to  pass  from  the 
concentrated  to  the  dilute  solution.  The  highest  valency  repre- 
sented by  the  ions  in  a  given  case  gives  the  value  of  v  directly.  If 
zinc  chloride  be  the  electrolyte,  v  =  2.  In  the  concentration  cell, 

Tl  -  T12S04  sol.,  cone.  -  T12S04  sol.,  dilute  —  Tl, 
v  is  also  equal  to  2.     If  the  electrolyte  be  thallium  nitrate,  v  =  1, 


200  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

and  so  on.  The  number  of  ions  formed  from  a  molecule  of  the 
electrolyte  is  nt. 

For  dilute  solutions  the  relation  between  the  concentrations  may 
be  used,  instead  of  that  between  the  osmotic  pressures.  For  ex- 
ample, in  the  cell, 

Ag  -  AgN03  sol.,  0.01  Cn  -  AgN03  sol.,  0.001  Cn  -  Ag, 

•p 

the  value  10  may  be  substituted  for  —  in  the  equation,  and  the 

*i 

value  of  the  electromotive  force  so  obtained  should  agree  closely 
with  that  measured. 

Nernst  l  measured  the  electromotive  force  of  the  cell, 

Ag  -  AgN03  sol.,  0.1  Cn  -  AgN03  sol.,  0.01  Cn  -  Ag, 
and  found,  at  18°  t,  F  =  0.055  volt. 

From  conductivity  measurements,  it  was  calculated  that  the  ratio  of 
the  two  concentrations  of  silver  ions,  instead  of  being  1  :  10  was 
1:8.71.  Hence  the  calculated  value  of  the  electromotive  force  is 
as  follows:  — 

F  =  0.000198  x  291  log  8.71  =  0.054  volt. 

In  this  calculation  it  was  assumed  that  the  transference  numbers  of 
the  anion  and  cation  are  equal.  If  the  fact  that,  instead  of  the  two 
values  being  equal,  the  value  of  the  transference  number  of  the 
nitrate  ion  is  0.53  is  taken  into  consideration,  the  calculated  value 
of  the  electromotive  force  becomes 

F  =  0.057  volt. 

Hence  the  agreement  between  the  calculated  and  the  experimen- 
tally found  value  is  very  satisfactory. 

The  following  statements  will  serve  to  give  a  general  idea  of  the 
magnitude  of  the  numerical  values.  Since  at  17°,  when 

nt  =  2  and  na  =  0.5, 


it  follows,  where  the  concentrations  of  the  ions  to  be  considered  are 
in  the  ratio  1  :  10  and  the  metal  univalent,  that 


F  =  0.0575  volt. 

1  Ztschr.  phys.  Chem.,  4,  129  (1889). 


ELECTROMOTIVE  FORCE  201 

If  the  ratio  of  the  concentrations  is  increased  to  1 : 100  or  1 : 1000, 
the  value  of  F  becomes  twice  or  three  times  as  great,  since  F  in- 
creases in  logarithmic  ratio. 

It  may  be  stated  in  general,  that  if  a  concentration  cell  involving 
univalent  ions  possesses  an  electromotive  force, 

F  =  a  x  0.0575, 

under  the  conditions  stated  above,  the  ratio  of  its  ion  concentra- 
tions is, 

,.,..-,,  o=1(K  ;g|||;||:^ 

If  the  ion  be  other  than  univalent,  the  corresponding  values  must 
be  divided  by  the  valency.  Thus  the  cell  consisting  of  copper  and 
copper  sulfate  solutions,  in  which  the  concentrations  of  the  copper 
ions  are  1 :  10,  would  give  an  electromotive  force  of  about  one  half 
that  of  the  corresponding  silver  concentration  cell.  Measurements 
by  Moser  corroborate  this  statement. 

The  equation  used  above  for  the  calculation  of  the  electromotive 
force,  which  is  sometimes  known  as  the  Nernst  equation,  appears  to 
hold,  not  only  for  aqueous  solutions,  but  also  for  solutions  in  fused 
salts.  At  least,  Gordon1  has  measured  the  electromotive  forces  of 
different  concentration  cells  of  silver  nitrate,  dissolved  in  a  fused 
mixture  of  potassium  and  sodium  nitrates,  at  temperatures  between 
200°  and  300°  £,  and  found  that  the  values  of  the  electromotive  force 
calculated  by  means  of  the  above  equation,  under  the  assumption  of 
complete  dissociation,  agree  with  the  values  found  by  experiment. 
He  observed  further,  that  when  the  concentration  of  the  silver 
nitrate  was  greater  than  ten  per  cent,  the  value  found  by  experiment 
was  always  less  than  the  calculated  value.  This  indicates  an  appre- 
ciably incomplete  dissociation  at  this  concentration. 

Concentration  cells  are  involved  in  most  electrolytic  work,  espe- 
cially in  metal  refining  and  in  galvanoplastic  work.  In  these  cases 
the  solution  becomes  more  concentrated  about  one  electrode,  and  less 
concentrated  about  the  other.  When  the  stirring  is  insufficient,  the 
electromotive  force  of  the  concentration  cell  which  results  may  be  of 
a  considerable  magnitude.  Since  this  force  must  be  overcome  by 
the  electromotive  force  of  the  primary  current,  energy  is  thus  un- 
necessarily lost.  Furthermore,  disturbances  due  to  the  decrease  in 
the  ion  concentration  about  the  cathode  may  injure  the  quality  of 
the  deposition  of  metal.  Concentration  cells  may  even  be  formed 

1  Ztschr.phys.  Chem.,  28,  302  (1899). 


202  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

at  one  electrode  alone  when  the  current  is  not  evenly  distributed. 
Such  cells  may  make  themselves  unpleasantly  evident  by  causing 
the  metal  already  deposited  to  redissolve  in  places.  This  is  con- 
firmed by  the  following  simple  experiment:  If  a  dilute  layer  is 
placed  above  a  concentrated  layer  of  stannous  chloride  solution  in  a 
test  tube  containing  a  rod  of  tin,  it  will  be  observed  that  the  part  of 
the  rod  in  contact  with  the  dilute  solution  is  very  soon  eaten  into, 
while  crystals  of  tin  separate  out  on  the  part  in  contact  with  the 
concentrated  solution.  The  formation  of  concentration  cells  at  one 
electrode  can  be  prevented  by  an  efficient  stirring  of  the  solution. 

The  fact  that  standard  cells  can  only  be  used  for  small  current 
densities  may  now  be  understood.  Because  of  the  slight  solubility 
of  the  mercury  salts  used  in  them,  the  concentration  of  the  ions  is 
very  small.  Moreover,  the  ions  removed  from  the  solution  by  the 
passage  of  the  current  are  but  slowly  replaced  from  the  excess  of 
solid  salt.  Consequently,  the  electromotive  force  of  the  cell  must 
decrease  when  it  produces  a  considerable  current.  While  at  the 
cathode  a  state  of  under  saturation  is  produced,  at  the  anode  the 
solution  becomes  slightly  supersaturated.  When  the  cell  is  allowed 
to  remain  inactive  for  a  time,  the  concentrations  of  the  solution 
about  the  two  electrodes  change  spontaneously  until  the  original 
uniform  value  is  reached.  This  discussion  leads  directly  to  the  con- 
sideration of  a  second  kind  of  concentration  cells. 

b.  A  type  of  this  kind  of  concentration  cells  is  represented  by  the 
combination, 

Ag  —  AgN03  sol.  —  KC1  sol.  —  Ag  (covered  with  AgCl). 

In  spite  of  the  apparent  differences  between  this  and  the  cell  last 
described,  the  two  are  entirely  analogous.  In  the  calculation  of  the 
electromotive  force  only  the  osmotic  pressures  of  the  silver  ions  in 
the  nitrate  solution  and  in  the  solution  of  the  silver  chloride  require 
to  be  taken  into  account.  The  potassium  chloride  is  used  merely  to 
increase  the  conductivity  of  the  silver  chloride  solution.  In  practice 
a  solution  of  potassium  nitrate  is  inserted  between  the  potassium 
chloride  and  silver  nitrate  solutions,  in  order  to  prevent  the  forma- 
tion of  a  precipitate.  The  equation 

^0.0001983^1 
holds  good. 

r> 

In  the  calculation  of  F  the  ratio  --  alone  need  be  known.     The 


ELECTROMOTIVE  FORCE  203 

value  of  v  in  this  case  is  unity.  In  the  nitrate  solution  the  concen- 
tration of  the  silver  ions  may  be  known,  if  a  solution  of  a  certain 
strength  be  prepared;  for  if  not  very  dilute,  so  that  complete 
dissociation  may  be  assumed,  the  degree  of  dissociation  may  be 
determined.  In  the  case  of  the  solution  of  silver  chloride,  the 
concentration  of  silver  ions  is  not  so  easily  ascertained.  On  account 
of  the  slight  solubility  of  the  chloride,  it  is  certainly  very  small. 
By  means  of  the  electrical  conductivity  (page  137),  the  solubility  in 
pure  water  may  be  determined.  It  has  thus  been  found  that  the 
saturated  silver  chloride  solution  at  25°  is  0.0000144  normal.  In 
such  a  dilute  solution  the  salt  is  doubtless  practically  all  dissociated 
into  the  ions,  Ag'  and  Clf;  moreover,  as  they  are  present  in  equiva- 
lent amounts,  the  solution  is  0.0000144  normal  in  respect  to  silver  or 
chlorine  ions,  and  the  product  of  these  concentrations  is 

Ag  x  CI'  =  (0.0000144)2  =  S2        / 

when  S  represents  the  solubility  of  the  salt. 

Instead  of  a  pure  aqueous  solution  of  silver  chloride,  that  of  the 
cell  also  contains  potassium  chloride.  From  page  202  it  is  seen  that 
the  product  of  the  concentrations  of  the  ions,  divided  by  the  con- 
centration of  the  undissociated  molecules,  is  a  constant  independent 
of  the  dilution,  or, 

CAK'   X  CCT__  -rr 
-(=, A* 

t-'AgCl 

and,  since  in  a  saturated  solution  the  undissociated  portion  must  be 
considered  to  remain  constant,  the  same  is  true  also  of  the  product 
of  the  concentrations  of  the  ions,  or 

@AK'  X  C/ci'  =  K. 

When  a  relatively  large  amount  of  potassium  chloride  is  added 
to  a  saturated  aqueous  silver  chloride  solution,  the  number  of 
chlorine  ions  is  greatly  increased,  and,  in  consequence,  a  certain 
amount  of  undissociated  silver  chloride  must  form  and  be  precipi- 
tated, since  the  solution  is  already  saturated  with  it.  If  C  is  the 
concentration  of  the  silver  ions  after  the  addition,  and  also  that  of 
the  chlorine  ions  derived  from  the  silver  chloride,  while  Ci  is  the 
concentration  of  the  added  chlorine  ions,  then 

C(C+Ci)  =  S», 

and  since  Ci  is  very  great  compared  with  (7,  the  equation  may  be 

written  Q2 

t     o 


204  A   TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

To  obtain  the  concentration  of  the  ion  corresponding  to  the  mate- 
rial of  the  electrode,  the  square  of  the  solubility  S  of  the  salt  used 
is  divided  by  the  concentration  of  the  other  ion,  of  which  an  excess 
is  added.  Supposing  a  0.1  normal  potassium  chloride  solution  to  be 
used,  Ci  for  complete  dissociation  would  be  0.1,  but  since  at  this 
concentration  it  is  only  about  85  per  cent  dissociated,  d  =  0.085; 

and  therefore 

c==(0.0000144)2 

0.085 

Since  the  osmotic  pressures  are  proportional  to  the  concentrations, 
and  the  silver  nitrate  is  82  per  cent  dissociated,  when  the  silver 
nitrate  solution  is  0.1  <7n,  the  following  holds  for  25°  t  :  — 


-  0.000198  x  298  x  log  =  0.44  volt. 


The  corresponding  value,  experimentally  determined  by  Goodwin, 
is  0.45  volt.     The  agreement  is  satisfactory. 

The  following  arrangement  is  another  example  of  such  cells  :  l  — 

Ag  -  KN03  sol.,  sat.  with  AgBr03  ------  7 

Ag  -  KBrO3  sol.,  sat.  with  AgBr03  ______  1' 


The  concentration  of  the  silver  ions  in  the  nitrate  solution  is  nearly 
the  same  as  in  pure  water,  since  the  nitrate  yields  neither  Ag  nor 
Br03  ions,  and  consequently  has  but  slight  influence  on  the  state  of 
dissociation  of  the  AgBr03.  The  concentration  of  the  silver  ions  in 
the  potassium  bromate  solution  may  be  calculated  as  before,  from 
the  solubility  of  the  silver  bromate  in  water  and  the  concentration 
of  the  Br03  ions  added.  When  the  values  so  obtained  are  substi- 
tuted in  the  formula, 

F  =  0.0612  volt  for  0.1  <7W, 
and  F  =  0.0454  volt  for  0.05  On 

solution  of  potassium  bromate  solution.  The  experimentally  deter- 
mined magnitudes  are  0.0620  and  0.0471.  The  current,  as  before, 
passes  through  the  cell  from  the  weaker  to  the  more  concentrated 
solution  of  silver  ions,  i.e.  from  the  bromate  to  the  nitrate  solution. 
Electrodes  in  which  the  metal  is  in  contact  with  one  of  its  diffi- 
cultly soluble  salts,  and  also  in  the  presence  of  a  solution  of  a  soluble 
salt  with  the  same  negative  ion,  were  called  by  Nernst  electrodes  of 
the  second  order,  or,  as  regards  the  negative  ions,  reversible  elec- 

1  Ztschr.  phys.  Chem.,  13,  577  (1894). 


ELECTROMOTIVE   FORCE  205 

trodes.  Ostwald  showed  that  these  are  not  to  be  distinguished  from 
metal  electrodes  in  a  solution  of  one  of  their  salts. 

c.  A  third  kind  of  concentration  cell  consists  of  those  in  which 
one  of  the  electrolytes  is  a  complex  salt.  As  a  type  of  this  class, 
the  following  combination  may  be  given  :  — 

Ag  -  AgN03  sol.  -  KCN  sol.  (+  a  little  AgCN)  -  Ag. 

In  the  latter  solution  the  complex  salt  KAg(CN)2  is  formed,  the 
ions  being  K'  and  Ag(CN)2  '.  This  negative  ion  is  in  turn  dissoci- 
ated to  an  extremely  slight  extent  into  2(CN)'  and  Ag',  and  it  is  the 
concentration  of  this  latter  silver  ion  which,  in  this  solution,  is  to 
be  taken  into  account  in  considering  the  electromotive  force  of  the 
cell.  It  is  evidently  somewhat  dependent  upon  the  quantity  of 
silver  cyanide.  Since  it  is  at  present  impossible  to  measure  the 
concentration  of  this  small  quantity  of  ions  in  the  solution  of  the 
complex  salt  by  an  independent  method,  it  is  impossible  to  calculate 
the  electromotive  force  of  such  cells.  On  the  other  hand,  the  meas- 
urement of  the  electromotive  force  gives  a  means  of  calculating  the 
concentration.  This  is  also  true,  naturally,  of  the  cell  previously 
described. 

The  calculation  of  the  concentration  from  the  measured  electromo- 
tive force  will  now  be  carried  out  for  the  parallel  case  of  the  cell,1 


Hg-HgN03  solution,  0.1  C 

Hg  —  Hg2S  dissolved  in  Na^S  solution  -----  • 


n- 


The  value  of  the  electromotive  force  at  17°  t  was  found  to  be  1.252 
volts.     Hence, 


1.252  =  0.000198  x  290  log  C, 


P 
P' 


where  P  and  P  may  represent  either  the  osmotic  pressures,  or  the 
concentrations  of  the  mercury  ions  in  the  nitrate  and  sulfide  solu- 
tions. Furthermore, 

log      = 


p  21.8 

and  —  =  10     • 

PI 

Assuming  complete  dissociation,  there  are  20  grams  of  mercury 
ions  in  a  liter,  or  1  mg.  of  ion  in  0.00005  liter,  of  the  0.1  normal 

1  Behrend,  Ztschr.  phys.  Chem.,  11,  466  (1893);  see  also  Ztschr.  phys.  Chem., 
15,  495  (1894). 


206  A   TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

mercurous  nitrate  solution.  This  latter  number,  multiplied  by  1021-8, 
gives  the  number  of  liters  of  the  sodium  sulphide  solution  contain- 
ing 1  milligram  of  mercury  ions. 

A  means  of  determining  the  solubility  of  the  difficultly  soluble 
salts,  and  thereby  the  ion  concentration,  has  already  been  found  in 
the  measurement  of  electrical  conductivity.  These  considerations 
furnish,  however,  a  second  method  far  surpassing  the  first  in  deli- 
cacy. In  fact,  it  is  exactly  at  those  extremely  low  concentrations, 
where  all  other  methods  are  without  avail,  that  the  advantages  of 
this  one  are  most  prominent,  since  the  electromotive  force  becomes 
higher  the  greater  the  difference  in  the  concentrations.  In  order  to 
avoid  error,  however,  what  has  been  said  on  page  163  in  regard  to 
the  capacity  of  the  measuring  instruments  must  be  borne  in  mind. 

Extrapolations  such  as  the  above l  into  the  domain  of  extremely 
small  ion  concentrations  are  naturally  accompanied  with  some  un- 
certainty, since  it  is  tacitly  assumed  that  the  regularities  which 
have  been  found  to  exist  in  the  case  of  ions  of  moderate  concentra- 
tion also  exist  in  the  case  of  ions  of  such  small  concentrations. 
Moreover,  that  the  formation  of  potential  and  the  activity  of  such 
cells  can  depend  upon  such  slight  concentrations  of  the  metal  ions 
is  scarcely  conceivable.  It  would  seem  necessary  to  ascribe  an 
active  part  to  the  complex  ions.  Nevertheless,  as  will  be  shown  in 
the  section  on  the  formation  of  potential  at  the  electrodes,  as  long 
as  it  is  assumed  that  the  concentrations  of  the  various  substances, 
including  the  ions,  are  always  related  in  a  definite  manner,  and  are 
in  equilibrium  with  each  other  according  to  the  law  of  mass  action, 
the  calculation  of  the  potential  is  the  same  whichever  the  actual 
process  taking  place  at  the  electrode  may  be.  Bearing  this  in  mind, 
it  may  be  said  that  the  measured  values  of  the  potentials  correspond 
to  the  calculated  small  ion  concentrations. 

Attention  may  be  called  to  the  following  important  fact :  In  the 
three  cells,  — 

^  Silver  —  AgN03  solution,  0.1  Cn , 

*  Silver -KC1  solution,  0.1  Cn  saturated  with  AgCl-1' 

2  Silver  -  AgN03  solution,  0.1  Cn , 

'  Silver  —  KBr  solution,  0.1  Cn  saturated  with  AgBr.-J.' 


Silver  -  AgNOg  solution,  0.1  CB 

Silver  —  KI  solution,  0.1  Cn  saturated  with  Agl 


1  See  the  discussion  between  Haber,  Bodlander,  Abegg,  and  Danneel,  Ztschr. 
Mektrochem.,  10,  403,  604,  607,  609,  and  773  (1904). 


ELECTROMOTIVE  FORCE  207 

the  electromotive  force  increases  from  the  first  to  the  third 
cell. 

This  is  a  consequence  of  the  fact  that  the  silver  chloride  is  more 
soluble  than  the  bromide,  and  this  in  turn  more  soluble  than  the 
iodide,  and  of  the  fact  that  all  three  salts  are  practically  completely 
dissociated  in  their  saturated  solutions.  In  such  cells  as  these  the 
electromotive  force  is  greater  the  less  soluble  the  salt.  With  the 
complex  instead  of  the  insoluble  salts,  as  is  illustrated  by  the  0.1 
normal  potassium  cyanide  solution,  to  which  some  silver  cyanide 
was  added,  the  electromotive  force  is  the  greater  the  fewer  the  metal 
ions  furnished  by  the  salt  (in  this  case  silver).  If  a  series  of  such 
cells  be  arranged  in  the  order  of  their  electromotive  forces,  begin- 
ning with  the  lowest,  the  order  is  also  that  of  the  solubility,  or  of 
the  decomposition.  Each  salt  in  the  series  will  dissolve  in,  and 
will  react  with,  any  of  the  saturated  solutions  of  the  cells  following 
in  the  series.  For  example,  silver  chloride  added  to  the  potassium 
bromide  solution  forms  silver  bromide ;  silver  bromide  in  the  potas- 
sium iodide  solution  forms  silver  iodide,  etc.  When  silver  cyanide 
is  added  to  a  solution  of  sodium  sulfide,  it  is  changed  into  silver  sul- 
fide  because  the  electromotive  force  of  the  cell, 

Silver- AgNOg  solution, 0.1  Cn- . 

Silver  -  Na2S  solution,  0.1  Cn  saturated  with  Ag2S—  -! ' 

is  greater  than  that  of  the  corresponding  cyanide  cell.  On  the 
other  hand,  silver  sulfide  does  not  dissolve  in  dilute  potassium 
cyanide  solution.  The  reason  for  this  is  easily  seen  when  it  is 
remembered  that  the  more  insoluble  or  complex  a  salt  is,  the 
lower  is  also  the  value  of  the  product  of  the  corresponding  ions.  If 
to  a  saturated  silver  chloride  solution  an  amount  of  iodine  ions  (as 
in  potassium  iodide)  be  added  equal  to  the  chlorine  ions  present, 
silver  iodide  must  precipitate ;  otherwise  the  product  of  concentra- 
tion of  the  iodine  and  silver  ions  would  be  greater  than  its  stable 
value.  The  concentration  of  the  ions  must,  then,  decrease  in  the 
only  way  possible,  i.e.  by  the  precipitation  of  solid  silver  iodide.  This 
precipitation  proceeds  until  the  product  of  the  ion  concentrations  has 
reached  the  constant  value  corresponding  to  the  saturated  silver 
iodide  solution. 

Such  an  arrangement  of  concentration  cells  is  given  in  the  follow- 
ing table:1 — 

iQstwald,  Lehrb.  der  Allg.  Chemie  II,  1,  882. 


208  A  TEXT-BOOK  OF   ELECTRO-CHEMISTRY 


SILVER  NITRATE,  0.1  Cn  AGAINST  — 


F,  IN  VOLTS 


Silver  chloride,  in  potassium  chloride  of  1  Cn 
Ammonia,  1  Cn  •  •         • 

Silver  bromide,  in  potassium  bromide  of  1  <?„ 
Sodium  thiosulfate,  1  <7»  .        . 

Silver  iodide,  in  potassium  iodide  of  1  Cn 
Potassium  cyanide  solution 
Sodium  sulfide,  1  Cn  . 


0.51 
0.54 
0.64 
0.84 
0.91 
1.31 
1.36 


A  few  drops  of  silver  nitrate  solution  were  added  to  the  solutions 
of  ammonia,  sodium  thiosulfate,  and  potassium  cyanide,  respectively. 

Evidently  the  order  of  such  a  series  may  be  changed  by  altering 
the  concentrations  of  the  electrolytes  added  to  the  silver  salts.  This 
might  be  done,  for  example,  by  adding  a  very  concentrated  solution 
of  potassium  chloride  to  the  silver  chloride  solution  ;  the  concentra- 
tion of  the  silver  ions  would  thus  be  reduced  below  that  of  the  0.1 
normal  bromide  solution,  which  contains  silver  bromide.  In  this 
case  the  electromotive  force  of  the  chloride  cell  would  be  greater 
than  that  of  the  bromide,  and  even  if  0.1  normal  potassium  bromide 
solution  be  added  to  the  chloride  solution,  silver  bromide  would  not 
be  precipitated ;  on  the  other  hand,  silver  bromide  could  be  dissolved 
in  it.  Similarly,  silver  sulphide  would  dissolve  in  concentrated 
potassium  cyanide  solution. 

d.  Finally,  a  concentration  cell,  which  might  also  be  included 
under  description  a,  may  be  here  considered,  because  of  its  peculiar 
characteristics.  Attention  was  first  called  to  it  by  Ostwald.  A  cell 
consisting  of  one  hydrogen  electrode  in  an  acid  solution,  and  another 
in  an  alkali  solution,  the  two  solutions  being  in  contact,  is  a  concen- 
tration cell  with  regard  to  hydrogen  ions.  It  has  already  been 
learned  that  water  is  slightly  dissociated  into  H  and  OH  ions,  and 
consequently  a  certain  quantity  of  H  ions  is  present  in  the  alkali 
solution.  The  electromotive  force  of  this  cell  is 

ET  .     P 

F  = In—, 

Q  P! 

P  being  the  concentration  or  osmotic  pressure  of  the  hydrogen  ions 
in  the  acid  solution,  and  Pl  that  of  the  ions  in  the  alkali.  Suppose 
the  alkali  and  acid  used  to  be  normal  solutions.  The  concentration 
P  of  the  H  ions  in  the  acid  solution,  when  the  incomplete  disso- 
ciation is  taken  into  account,  is  about  0.8,  and  Pl  may  be  calculated 
from  the  measured  electromotive  force  of  the  cell.  In  this  case  a 
considerable  potential-difference  exists  at  the  surface  of  contact  be- 


ELECTROMOTIVE  FORCE  209 

tween  the  two  solutions,  which  must  be  taken  into  consideration, 
since  the  sum  of  the  potentials  at  the  electrodes  alone  is  desired. 
With  the  correction  given  by  Nernst,1  the  value  of  F  at  18°  is  0.81 
volt  ;  that  is, 

0.81  =  0.0577  log  ~, 

£=>»"•• 

The  concentrations  of  the  hydrogen  ions  are  proportional  to  their 
respective  osmotic  pressures.     Then,  since 

O=0.8, 

the  value  of  the  concentration  of  the  hydrogen  ions  in  the  alkali 
solution  is  as  follows  :  — 

<7  =  0.8xlO-14. 

Now  according  to  the  law  of  mass  action,  the  product  of  the  hydro- 
gen and  hydroxyl  ions  must,  in  this  case  also,  give  a  constant  when 
divided  by  the  concentration  of  the  undissociated  water,  or, 


The  concentration  of  the  undissociated  water  is  so  great  in  compari- 
son with  that  of  the  ions,  that  it  may  be  considered  as  a  constant. 
Consequently,  the  product  of  the  concentrations  of  the  two  ions 
must  be  a  constant,  or, 

O(of  IT)  x  C  (of  OH')  =  const. 
But  the  concentration  of  the  hydrogen  ions  in  the  alkali  solution  is 

C"  =  0.8xlO-14, 
and  that  of  the  hydroxyl  ions,  according  to  the  supposition,  is 

O  =  0.8. 
Hence  O  X  O=  (0.8)2  x  10~14. 

From  this  result,  the  dissociation  of  water  may  be  directly  ascer- 
tained, for  the  product  of  the  concentrations  of  the  hydrogen  and 
hydroxyl  ions  in  pure  water  is  the  same  as  that  of  these  ions  in  an 
alkali  solution.  Hence,  for  pure  water, 

O(of  H')  x  O(of  OH')  =  (0.8)2  x  10-14. 
iZtschr.  phys.  Chem.,  14,  155  (1894). 


210  A   TEXT-BOOK   OF   ELECTRO-CHEMISTRY 

But,  in  this  case,  the  concentration  of  the  two  ions  is  the  sama 
Therefore,  if  G  represents  this  concentration, 

C2=(0.8)2xlO-14, 
or  C=0.8xlO-7. 

In  other  words,  pure  water  is  0.8  x  10~7  normal  with  respect  to  its 
hydrogen  or  hydroxyl  ions.  The  conductivity  measurements  of 
Kohlrausch  gave  0.75  x  10~7.  This  is  a  very  remarkable  agreement, 
and  its  significance  is  made  greater  by  the  fact  that  other  methods 
for  reaching  the  same  end,  as  through  the  study  of  the  hydrolysis 
of  salts  and  the  saponifying  effect  of  water,  have  led  to  very  nearly 
the  same  value. 

Oxygen  electrodes  may  be  used  instead  of  hydrogen,  and  the  cell 
still  have  the  same  electromotive  force,  because  the  concentrations 
of  the  hydrogen  ions  in  the  two  solutions  are  in  the  same  relation  to 
each  other  as  those  of  the  corresponding  hydroxyl  ions.  This  fol- 
lows from  the  fact  that  the  product  of  the  concentrations  of  the  H 
and  OH  ions  of  the  solutions  in  the  cell  is  a  constant.  The  fact 
that  the  platinum  does  not  absorb  oxygen  as  readily  as  it  does  hydro- 
gen, and  that  it  reaches  a  state  of  equilibrium  with  the  surrounding 
gas  more  slowly,  makes  it  more  difficult  to  obtain  constant  results. 
In  both  cases,  the  current  flows  through  the  cell  from  the  alkali  to 
the  acid  solution. 

It  may  be  repeated  here  that,  except  for  the  potential-difference 
existing  between  the  solutions  at  their  point  of  contact,  the  electro- 
motive force  of  such  cells  does  not  depend  upon  the  nature  of  the 
negative  ion  of  the  acid,  nor  upon  the  positive  ion  of  the  alkali.  On 
the  other  hand,  when  acids  of  the  same  molecular  concentrations 
are  used,  the  degree  of  dissociation  comes  into  play.  The  cell 


Hydrogen  —  Acetic  acid  solution 

Hydrogen  —  Potassium  hydroxide  solution- 


would  exhibit  a  lower  electromotive  force  than  the  cell  of  correspond- 
ing concentrations, 


Hydrogen  —  Hydrochloric  acid  solution — 
Hydrogen  —  Potassium  hydroxide  solution- 


The  slightly  dissociated  acetic  acid  contains  less  hydrogen  ions  than 
the  highly  dissociated  hydrochloric  acid;  consequently  in  the  latter 
cell  the  difference  in  concentration  between  the  hydrogen  ions  of  the 
acid  and  alkali  solutions  is  greater  than  in  the  former,  and  there- 


ELECTROMOTIVE  FORCE  211 

fore  its  electromotive  force  is  also  greater.  That  the  same  consid- 
erations apply  to  bases  may  be  safely  concluded  from  the  measure- 
ments which  have  already  been  made  in  that  direction. 

3.  Concentration  Double-Cells.  —  Another  kind  of  concentration 
cell  may  be  formed  by  combining  two  simple  cells  into  a  double- 
cell.  The  so-called  calomel  cell,  which  is  very  often  used,  serves  as 
a  type  of  such  a  double-cell.  Its  combination  is  as  follows :  — 


Zn  —  ZnCl2  solution,  cone. 

^    /HgCl  solution,  sat. 

g\HgCl  solution,  sat- 

Zn  —  ZnCl2  solution,  dil 


The  mercurous  chloride  is  in  excess,  and  covers  the  mercury. 
This  cell  differs  from  the  simple  cell, 

Zn  —  ZnCl2  solution,  cone.  —  ZnCl2  solution,  dil.  —  Zn, 
in  having  the  combination,  — 

HgCl-Hg-HgCl, 

between  its  two  differently  concentrated  solutions  of  zinc  chloride. 
Consequently,  the  processes  of  electrolysis  and  the  electromotive 
forces  of  such  double-cells  differ  from  those  of  the  simpler  cells.  In 
the  case  of  the  simple  cell,  when  2g  coulombs  of  electricity  pass, 
there  is  a  migration  of  zinc  and  chlorine  ions  from  one  solution  to  the 
other,  and  a  simultaneous  solution  and  precipitation  of  two  equiva- 
lents of  zinc  at  the  electrodes.  In  the  calomel  concentration  cell  such 
a  migration  cannot  occur.  When  2  Q  coulombs  pass  through  this  cell, 
two  equivalents  of  zinc  dissolve  in  the  dilute  chloride  solution,  and 
two  of  mercury  separate  from  the  mercurous  chloride.  Here  the 
current  always  passes  from  the  dilute  to  the  concentrated  solution 
within  the  cell.  The  mercury  ions  come  from  the  dissolved  mercu- 
rous chloride,  and  those  precipitated  are  immediately  replaced  by 
the  further  solution  of  mercurous  chloride.  In  the  concentrated 
solution,  on  the  other  hand,  two  equivalents  of  zinc  separate  at  the 
electrode,  and  two  of  mercury  are  dissolved.  It  must  be  borne  in 
mind  that  when  two  equivalents  of  metallic  mercury  have  been  pro- 
duced from  the  solid  mercurous  chloride  in  the  dilute  solution,  two 
equivalents  of  chlorine  ions  have  also  been  formed ;  and  when  two 
equivalents  of  metallic  mercury  have  changed  to  mercurous  chloride 
in  the  concentrated  solution  at  the  same  time,  two  of  chlorine  ions 
have  disappeared.  When  the  quantities  of  the  solutions  are  imag- 


212  A   TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

ined  so  great  that  these  changes  take  place  without  sensible  influ- 
ence on  the  concentration,  the  processes  may  be  summarized  as 
follows  :  Two  equivalents  of  zinc  and  two  of  chlorine  —  that  is,  one 
mol  of  zinc  chloride  —  have  been  transferred  from  the  concentrated 
solution  to  the  dilute,  while  the  quantity  of  mercury  and  of  mercu- 
rous  chloride  remains  unaltered.  If  the  osmotic  pressure  of  the 
zinc  ions  in  the  concentrated  solution  be  P,  and  in  the  dilute  solu- 
tion PU  then  the  corresponding  osmotic  pressures  of  the  chlorine 
ions  are  2  P  and  2  Pj.  The  maximum  osmotic  work  is  easily  calcu- 
lated, and  is  given  by  the  equation, 

Wo,  =  RT  In  —  +2  RTln  —  =  3  RTlu  —  • 
PI  2  P!  P! 

The  electrical  energy  is  2  FQ,  therefore 


_ 

2    2Q         Px 

In  general,  F  ==  ^-  —  In  —  , 

v    Q        P! 

where  n{  is  the  number  of  ions  formed  from  one  molecule  of  the 
electrolyte,  and  v  the  number  of  electrochemical  units  Q  required 
to  transfer  one  mol  of  the  electrolyte  from  the  concentrated  to  the 
dilute  solution.  It  is  evident  from  a  comparison  of  this  equation 
with  that  given  on  page  199  that  here  we  have  another  method  for 
the  calculation  of  the  transference  numbers  of  an  electrolyte. 

p 
From  the  formula  it  may  be  seen  that  only  the  ratio  -^  ,  niy  and 

-*i 
v  have  influence   on  the  value  of  the  electromotive  force  F.     As 

Ostwald  predicted,  and  as  Goodwin  *  experimentally  demonstrated, 
it  follows  that  :  — 

1.  The  mercurous  chloride  and  mercury  of  the  calomel  cell  may 
be  replaced  by  silver  chloride  and  silver  without  altering  the  electro- 
motive force. 

2.  Instead  of  zinc  chloride,  zinc  bromide  or  iodide  may  be  used 
when  the  depolarizer2  is   a  difficultly   soluble  bromide  or  iodide, 
without  changing  the  electromotive  force. 

3.  The  electromotive  force  of  the  cell  will  not  be  changed  if  cad- 
mium chloride  and  cadmium  be  substituted  for  zinc  chloride  and  zinc. 

iZtschr.phys.  Chem.,  13,  577  (1894). 

2  The  difficultly  soluble  salt  is  here  called  a  depolarizer,  because,  through  its 
presence,  the  electrode  is  made  unpolarizable  for  small  currents. 


ELECTROMOTIVE   FORCE 


213 


4.  If  the  zinc  and  zinc  chloride  be  replaced  by  thallium  and  thal- 
lium chloride,  the  electromotive  force  will  be  considerably  increased. 

5.  If  instead  of  the  chloride  of  zinc,  the  sulfate  be  used,  with  a 
difficultly   soluble   sulfate   as   depolarizer,  the  electromotive  force 
will  be  less  than  before.     Whether  lead  or  mercurous  sulfate  be 
used  as  depolarizer  can  make  no   difference.     The  accompanying 
tables  confirm  these  statements.     For  the  sake  of  brevity  the  cells 
are  designated  by  their  soluble  salts  and  depolarizers. 


ZnCl2  -  HgCl  and  ZnCl2  -  AgCl  Cells  at  25 


CONCENTRATION 

OBSERVED  E.M.-F. 

OBSERVED  E.  M.  F. 

CALCULATED 

OF  THE  ZnClj 

OF  ZnCl2  -  HgCl 

OF  ZnCls  -  AgCl 

E.  M.  F.  IN  VOLTS 

0.2    -0.01 

0.0787 

0.0767 

0.0797 

0.1    -  0.01 

0.0800 

0.0780 

0.0818 

0.02  -  0.002 

0.0843 

0.0843 

0.0844 

0.01  -  0.001 

0.0861 

0.0847 

0.0853 

Considering  the  experimental  errors  of  1  to  2  thousandths  of  a  volt, 
the  agreement  is  very  satisfactory. 

, "    II 
ZnBr2  -  HgBr  and  ZnBr2  -  AgBr  Cells 


CONCENTRATION  OF 

OBSERVED  E.  M.  F. 

OBSERVED  E.  M.  F. 

CALCULATED 

THE  ZnHr2 

OF  ZnBr2  -  HgBr 

OF  ZnBr2  -  AgBr 

E.  M.  F.  IN  VOLTS 

0.2    -0.02 

0.0793 

0.0793 

0.0797 

0.1    -0.01 

0.0808 

0.0802 

0.0818 

0.02  -  0.002 

0.0860 

0.0852 

0.0862 

0.01  -  0.001 

0.0863 

0.0858 

0.0853 

Through  replacement  of  zinc  and  its  chloride  by  cadmium  and 
cadmium  chloride,  the  value  of  the  electromotive  force  could  not  be 
calculated,  the  concentration  of  the  cadmium  ions  not  being  deter- 
minable  with  exactness  (by  the  conductivity  method).  This  is  ex- 
plained by  the  fact  that  CdCl2  dissociates  not  only  into  Cd"  and  Cl', 
Cl',  but  probably  also,  in  concentrated  solutions,  into  CdCl'  and  Clf. 
In  dilute  solutions,  where  only  the  former  dissociation  is  consider- 
able, the  values  calculated  agree  with  those  experimentally  found. 


214 


A  TEXT-BOOK   OF   ELECTRO-CHEMISTRY 


III 

T1C1  -  HgCl  Cells 


CONCENTRATION 

OBSERVED 

CALCULATED 

OF  THE  T1C1 

E.M.F. 

E.  M.  F. 

0.0161  -  0.00161 

0.102 

0.114 

0.008    -0.0008 

0.100 

0.115 

0.0161  -  0.008 

0.0328 

0.033 

The  experimental  errors  in  this  case  are  greater  than  those  in  the 
two  previous  tables. 

IV 
ZnS04  -  PbS04  Cells 


CONCENTRATION 

OBSERVED 

CALCULATED 

OF  THE  ZnSO4 

E.M.F. 

E.M.F. 

0.2    -0.02 

0.0427 

0.0453 

0.1    -0.001 

0.0440 

0.0471 

0.02  -  0.002 

0.0522 

0.0500 

ZnS04  -  Hg2S04  Cells 


CONCENTRATION 

OF  THE  ZnS04 

OBSERVED 
E.M.F. 

CALCULATED 
E.M.F. 

0.2  -  0.02 
0.1  -  0.01 

0.047  -  0.034 
0.045  -  0.033 

0.045 
0.047 

The  formula 


«,  RT,    P 

F=  — In  — 

v     Q        Pi 


is  only  applicable  when  the  solubility  of  the  depolarizer  is  inappre- 
ciable. If,  for  example,  the  difficultly  soluble  mercurous  chloride 
of  the  calomel  cell  be  replaced  by  the  comparatively  easily  soluble 
thallium  chloride,  it  must  be  taken  into  account  that  the  concentra- 
tions of  the  zinc  and  the  chlorine  ions  are  no  longer  in  the  same  re- 
lation. Chlorine  ions  from  the  thallium  chloride  are  thus  added  to 


ELECTROMOTIVE   FORCE  215 

those  of  the  zinc  chloride,  and  from  the  law  of  mass  action  the  prod- 
uct of  the  ion  concentrations  of  the  thallium  and  chlorine  in  the 
saturated  thallium  chloride  solution  is  constant,  and  more  chlorine 
ions  must  enter  the  dilute  than  the  concentrated  zinc  chloride  solu- 
tion. From  this  consideration,  taking  into  account  the  previous 
deduction,  P  and  Pl  being  the  osmotic  pressures  or  the  concentra- 
tions of  the  zinc  ions,  and  P  and  P/  those  of  the  chlorine  ions, 

— 


(1) 

In  general,       VFQ  =  ntR Tin  ^  +  w/  ETlnj^, 

where  w,  and  n/  represent  the  number  of  cations  and  anions  which 
the  molecule  of  the  electrolyte  produces,  and  v  the  number  of  Q  units 
corresponding  to  the  transference  of  one  molecule  of  the  electrolyte 
from  the  concentrated  to  the  dilute  solution. 

The  electromotive  force  of  the  cell  may  also  be  calculated  from 
the  electrolytic  solution  pressures  of  the  two  metals  coming  into  con- 
sideration (in  the  calomel  cell,  the  zinc  and  mercury).  In  this  case 
the  electromotive  force  of  the  cell  consists  of  four  potential-differ- 
ences, existing  at  the  four  points  of  contact  between  metal  and 
liquid.  If  pzn  and  pHg  represent  the  solution  pressures  of  the  zinc 
and  mercury  respectively,  and  P,  P19  P,  and  P/  the  concentrations 
of  the  zinc  and  mercury  ions  in  the  concentrated  and  in  the  dilute 
solutions,  while  vZn  and  vHg  are  the  valencies  of  the  metals,  then 
taking  into  consideration  the  fact  that  the  current  passes  through  the 
cell  from  the  dilute  to  the  concentrated  solution,  the  electromotive 
force  is  represented  by  the  following  equation  :  — 


Q   \vzn      A       vHg      p^      vHg      P      vz 
This  may  be  shortened  to  the  form 


F=T(J  A+ln^y 

Equations  (1)  and  (2)  lead  to  the  same  result,  in  spite  of  their 


216  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

P' 

apparent  difference.     In  (1)  -—  represents  the  concentration  relation 

PI  p< 

of  all  the  negative  ions  of  the  solutions,  while  in  (2)  -p-  represents 

that  of  the  cations  of  the  depolarizer.  It  must  be  remembered  that 
saturated  solutions  of  the  depolarizer  are  being  considered;  conse- 
quently the  product  of  the  concentrations  of  all  the  anions  and  cat- 
ions of  the  depolarizer  is  a  constant  (the  anions  of  the  electrolyte 
and  depolarizer  being  always  alike,  as  in  the  case  of  ZnCl2  and 
HgCl).  The  separate  concentrations  are  also  in  a  definite  relation 
to  each  other.  When,  for  instance,  the  cations  and  anions  are  of  the 
same  valency,  as  in  the  example,  their  different  concentrations  in 
the  solutions  are  inversely  proportional  to  each  other.  If  the  anion 
be  bivalent  and  the  cation  univalent,  the  concentration  of  the  latter 
is  inversely  proportional  to  the  square  of  that  of  the  former,  and  so 
on.  This  explains  the  agreement  of  the  two  equations. 

Use  of  the  Electrometer  as  an  Indicator  in  Titration.  —  After  the 
explanation  of  the  above  concentration  cells,  the  interesting  use  of 
the  electrometer  as  an  indicator  will  be  easily  understood.  In  order 
to  illustrate  this  application,  consider  the  concentration  cell 

Ag  -  AgN03  sol.,  0.1  Cn-  AgN03  sol.,  0.1  Cn  -  Ag, 

the  electromotive  force  of  which  is  equal  to  zero.  If  to  one  of  the 
two  solutions  potassium  chloride  is  added,  the  difficultly  soluble 
precipitate,  silver  chloride,  is  formed,  the  concentration  of  the  silver 
ions  is  decreased,  and  an  electromotive  force  is  produced  in  the  cell. 
As  more  potassium  chloride  is  added,  the  electromotive  force  of  the 
cell  increases,  at  first  slowly,  then  faster  and  faster  until  a  sudden 
change  takes  place,  and  then  slowly  again.  This  behavior  may  be 
at  once  understood  from  a  consideration  of  the  equation, 

F  =  0.0575  log  ~, 

in  which  P  and  F  represent  the  two  concentrations  of  the  silver 
ions.  If,  for  example,  while  P  is  maintained  constant  the  value  of 
P1  is  decreased  to  one  hundredth  of  its  original  value,  the  electro- 
motive force  becomes 

F  =  2  x  0.0575  volt. 

In  order  to  produce  this  decrease  in  concentration,  it  would  be 
necessary  to  add  to  1000  cubic  centimeters  of  the  0.1  normal  solu- 
tion of  silver  nitrate  about  980  cubic  centimeters  of  a  0.1  normal 
solution  of  potassium  chloride,  if  both  solutions  are  completely  dis- 


ELECTROMOTIVE   FORCE  217 

aociated.  The  new  value  of  P'  may  be  decreased  to  one  hundredth 
of  its  value  by  the  further  addition  of  19.8  cubic  centimeters,  and 
the  value  of  P  so  obtained  may  be  decreased  to  the  same  extent  by 
the  addition  of  0.198  cubic  centimeter  of  0.1  normal  potassium 
chloride  solution,  etc.  With  each  successive  decrease  in  the  value 
of  P'j  the  electromotive  force  of  the  cell  is  increased  by  2  x  0.0575 
volt.  As  follows  from  what  has  just  been  stated,  the  greatest 
change  of  the  electromotive  force  with  the  addition  of  the  potas- 
sium chloride  solution  occurs  when  the  last  portion  of  silver  nitrate 
disappears,  or,  better  expressed,  when  the  concentrations  of  the 
silver  and  of  the  chlorine  ions  are  nearly  equal.  The  increase  of 
the  electromotive  force  with  further  additions  of  potassium  chloride 
is  very  slight,  being  due  to  the  decrease  of  the  silver  ions  by  the 
mass-action  effect  of  the  added  chlorine  ions.  When  the  original 
concentration  of  the  silver  is  known,  this  method  may  also  be  used 
for  the  determination  of  the  halogens.1  With  the  aid  of  two  hydro- 
gen electrodes  it  may  be  used  in  acid  and  alkali  titrations.2 

LIQUID  CELLS 

It  has  already  been  stated  in  the  consideration  of  the  concentra- 
tion cells  that  potential-differences  occur  at  the  points  of  contact 
between  the  solutions.  This  assumption  has  been  entertained  a 
long  time,  but  a  clear  conception  of  the  origin  of  such  potentials 
did  not  exist.  The  Becquerel  acid-alkali  cell  is  well  known ;  two 
platinum  electrodes  connected  together  are  placed  one  into  acid 
and  the  other  into  alkali  solution.  That  in  the  acid  becomes  posi- 
tively, and  the  other  negatively,  charged;  the  potential-difference, 
varying  with  the  conditions,  often  amounts  to  more  than  0.6  volt. 
Formerly  the  source  of  this  electrical  energy  was  erroneously 
thought  to  be  in  the  heat  generated  by  the  neutralization  of  the 
acid  and  alkali.  As  previously  explained,  this  is  practically  a  con- 
centration cell.  Oxygen  of  the  air  is  present  at  the  two  electrodes, 
and  in  the  acid  solution  there  are  few,  while  in  the  alkali  there  are 
many,  OH  ions.  Since  the  electrodes  are  of  ordinary  platinum 
instead  of  being  coated  with  platinum  black,  it  is  easily  explicable 
that  the  electromotive  force  of  such  a  cell  is  variable.  Ordinary 
platinum  does  not  absorb  oxygen  to  a  very  great  extent,  so  that  the 
condition  of  equilibrium  which  should  be  established,  in  which  the 
concentration  of  the  oxygen  dissolved  in  the  platinum  corresponds 

1  Ztschr.  phys.  Chem.,  11,  466  (1893). 

2  Ztschr.  phys.  Chem.,  24,  253  (1897). 


218  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

to  the  pressure  of  the  surrounding  oxygen,  as  in  the  case  of  plati- 
nized platinum,  is  practically  unrealizable;  consequently  the  cell 
has  an  uncertain  and  varying  value.  This  cell  cannot  generate  a 
perceptible  current,  because  the  quantity  of  oxygen  absorbed  by 
the  electrodes  is  very  small,  and,  being  exhausted,  is  replaced  by 
that  of  the  air  only  very  slowly.  The  presence  of  other  gases,  such 
as  hydrogen,  also  has  an  influence  upon  the  electromotive  force  of 
this  cell. 

We  are  indebted  to  Nernst1  for  satisfactory  explanations  of  the 
phenomena  of  these  liquid  cells,  their  theory  having  been  developed 
by  him.  If  a  solution  of  hydrochloric  acid,  for  example,  be  placed 
in  contact  with  a  more  dilute  solution  or  with  pure  water,  the  acid 
will  diffuse  into  the  water.  The  hydrogen  and  chlorine  ions  of  the 
acid  are,  to  a  certain  extent,  independent  particles  capable  of  mov- 
ing with  different  velocities  from  places  of  higher  osmotic  pressure 
to  those  of  lower.  Since  the  hydrogen  ions  migrate  more  rapidly 
than  those  of  chlorine,  the  foremost  of  the  diffusing  ions  are  hydro- 
gen, and  since  these  possess  positive  charges,  the  water  or  the  dilute 
solution  as  a  whole  exhibits  a  positive,  and  the  stronger  solution  a 
negative,  charge.  Owing  to  the  mutual  attraction  of  the  positive 
and  negative  charges  of  the  hydrogen  and  chlorine  ions,  this  sepa- 
rating process  does  not  actually  take  place  to  any  measurable  extent, 
the  hydrogen  ions  are  delayed,  and  the  chlorine  ions  increase  their 
speed,  so  that  a  condition  is  reached  in  which  both  migrate  at  the 
same  rate.  The  electrostatic  attraction,  as  well  as  the  potential 
difference  between  the  solutions,  exists  until  both  solutions  are 
homogeneous. 

The  unequal  velocities  of  migration  of  the  ions  are  therefore  the  cause 
of  the  potential-differences  at  the  contact  surfaces  of  differently  concen- 
trated solutions, 

If  the  negative  ions  have  the  greater  velocity  of  migration,  the 
more  dilute  solution  will  evidently  be  negative  to  the  concentrated. 
In  other  words,  the  dilute  solution  always  presents  the  electricity  of  the 
more  rapidly  moving  ion. 

Moreover,  it  is  thus  not  only  possible  to  foresee  the  nature  of 
the  potential-difference  at  the  point  of  contact  between  two  liquids, 
but  also  in  many  cases  quantitatively  to  calculate  the  magnitude 
of  such  potential-differences,  and  to  prove  the  calculations  by  actual 
experiment.  To  illustrate  this  point,  two  differently  concentrated 
solutions  of  an  electrolyte,  consisting  of  two  univalent  ions,  may 
be  imagined  in  contact.  Let  (1  —  na)  be  the  share  of  the  transport 
1  Ztschr.phys.  Chem.,  4,  129  (1889). 


ELECTROMOTIVE   FORCE  219 

of  the  positive  ion,  and  consequently  na  that  of  the  negative.  The 
quantity  of  electricity  Q  is  now  conducted  through  the  solutions  from 
the  concentrated  to  the  dilute,  then  (1  —  na)  positive  gram-ions  pass  from 
the  concentrated  into  the  dilute,  and  at  the  same  time  na  negative 
gram-ions  from  the  dilute  into  the  concentrated  solution.  Let  P 
represent  the  concentration  of  the  positive  and  negative  ions  in 
the  concentrated  solution,  and  Pl  the  same  in  the  dilute  solution. 
The  maximum  work,  the  process  being  completed  osmotically,  is 

W=  (1  -  wa)  RTln^  -  na  RTln  —, 

or  W=(l-2n 

P\ 

or  if  na  be  replaced  by  —  —  —  ,  uc  being  the  velocity  of  migration  of 
the  positive,  and  ua  that  of  the  negative,  ions, 


Consequently  F  =  Uc~u«  —  In  —  ,  (a) 

uc  +  ua    Q       pl 

because  FQ  =  W. 

If  uc  be  greater  than  ua,  the  electric  current  passes  from  the  con- 
centrated to  the  dilute  solution  in  the  cell  itself;  if  ua  be  greater 
than  uc,  the  current  passes  in  the  opposite  direction.  If,  finally, 
uc  =  ua,  no  potential-difference  exists  between  the  solutions,  and 
consequently  there  is  no  current. 

Nernst  constructed  such  liquid  oe-lls  so  that  the  potential  ob- 
served was  only  that  appearing  at  the  point  of  contact  of  two  solu- 
tions, and  compared  the  experimentally  determined  values  of  the 
electromotive  force  with  those  calculated  from  the  equation  derived 
above.  The  following  arrangement  was  used  :  — 

Hg-KCl  solution,  0.1  <?M,   sat.  with  HgCl- 

—  KCl,0.01Cn,- 
----------------  HC1,  0.01  Cn,  ----------- 


HC1,   0.1  Cn, 


-KC1  solution,  0.1  <7n,  sat.  with  HgCl-Hg. 

Since  the  two  ends  are  identical,  the  potential-differences  occurring 
there  neutralize  each  other,  and  therefore  only  those  differences  at 
the  four  contact  points  1,  2,  3,  and  4  are  to  be  taken  into  account. 


220  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

It  is  to  be  observed  that,  as  far  as  experience  has  gone,  the  rule 
holds  also  for  liquid  cells  that  only  the  ratio,  not  the  absolute  values  of 
the  osmotic  pressures,  comes  into  consideration.  (Nernst's  principle  of 
superposition.  Each  system  may  be  imagined  to  be  formed  from 
the  others  by  means  of  n-fold  superposition.)  Therefore  the  poten- 
tial-difference of  2  is  equal  and  oppositely  directed  to  that  of  4. 
Thus  the  potential-differences  at  1  and  3  alone  remain,  and  may  be 
calculated  from  the  above  formula.  If  u'c  and  u'a  are  the  velocities 
of  migration  of  the  potassium  and  chlorine  ions  respectively,  while 
u"c  and  u"a  (=  u'0  because  the  negative  ions  are  the  same)  are  the 
migration  velocities  of  the  hydrogen  and  chlorine  ions,  then  the  sum 
of  the  potential-differences  is  represented  by 


P        P' 

and  as  ^ 


therefore 


Uc  +  V  Q 


P  and  Pl  are  the  osmotic  pressures  or  concentrations  of  the  po- 
tassium and  chlorine  ions  in  the  concentrated  and  dilute  potassium 
chloride  solutions,  P'  and  P/  the  corresponding  values  of  the  hydro- 
gen and  chlorine  ions  in  the  corresponding  hydrochloric  acid  solu- 
tions. The  actual  measured  potential-difference  was  —0.0357  volt. 
The  negative  sign  is  used,  since  the  current  in  the  cell  flows  in  the 
direction  4  to  1,  and  since,  in  the  calculation,  it  has  been  considered 
positive  when  it  passed  from  the  concentrated  to  the  dilute  potas- 
sium chloride  solution.  The  potential-difference  resulting  from  cal- 
culation by  the  formula,  taking  into  consideration  the  incomplete 
dissociation  of  the  substances,  differs  from  the  above  by  about  four 
to  five  per  cent. 

The  equation  (a)  only  permits  of  calculation  of  the  potential-dif- 
ference at  the  points  of  contact  of  two  differently  concentrated 
solutions  of  one  and  the  same  binary  electrolyte.  If  it  is  desired  to 
make  it  applicable  to  electrolytes  whose  ions  have  different  valen- 
cies, it  takes  the  form 

£c_H« 
F_V y^RT^P 

~Uc  +  Ua      Q          P/ 

v  representing  the  valence  of  the  positive  and  vr  that  of  the  nega- 
tive ion. 


ELECTROMOTIVE   FORCE  221 

If  two  different  electrolytes  are  in  contact,  as,  for  instance, 
potassium  chloride  and  hydrochloric  acid,  the  calculation  is  more 
difficult.  Only  for  the  case  in  which  the  total  concentration  of  ions 
in  each  of  the  two  solutions  is  the  same,  the  following  simple  ex- 
pression holds:  — 

F  =  ^ln<  +  <S  (c) 

Q       u"c  +  u'a 

where  ufc  and  u'a  are  the  migration  rates  of  the  ions  of  one  electro- 
lyte, u"c  and  u"a  those  of  the  other.  The  electromotive  force  is  here 
independent  of  the  ratio  of  the  concentrations. 

The  calculation  is  still  more  difficult  when  one  of  the  electrolytes 
contains  polyvalent  ions.  If  all  the  ions  of  the  two  solutions  of 
binary  electrolytes  are  polyvalent  and  of  the  same  valency,  then 
when  the  ion  concentrations  are  the  same, 


VQ       u 

It  is  worthy  of  special  attention  that  in  general  there  can  be  no 
arrangement  of  solutions  in  an  electromotive  series  such  as  Volta 
formed  for  the  metals.  This  is  evident  from  the  fact,  already  men- 
tioned, that  such  solution  cells  as  the  one  measured  by  Nernst  (see 
pages  219  and  220)  produce  a  current.  A  circuit 
consisting  of  metals  only,  at  a  common  tempera- 
ture, does  not  generate  an  electric  current.  If, 
on  the  other  hand,  the  solutions  of  the  above 
cell,  without  the  mercury  and  the  mercurous 
chloride,  be  arranged  in  a  circuit  as  shown  in 
Figure  45,  an  electric  current  is  obtained  whose 
electromotive  force  is  that  previously  calculated.  FlQ  45 

The  existence   of  this  current  may  be  demon- 
strated by  its  power  of  induction,  and  it  lasts  until  the  concentra- 
tion of  the  various  ions  is  the  same  throughout  the  system. 

The  law  of  electromotive  series  applies  only  to  differently  concen- 
trated solutions  of  the  same  electrolyte  in  juxtaposition.  That  it 
holds  in  this  case  may  be  shown  by  adding  the  potential-differences 
occurring  at  the  different  points  of  contact,  and  comparing  the  sum 
with  the  potential-difference  actually  observed  between  the  first  and 
last  solutions  placed  directly  in  contact.  The  intermediate  members 
of  the  series  are  thus  shown  to  play  no  part. 

In  considering  concentration  cells,  such  conditions  were  usually 
chosen  that  the  potential-differences  occurring  at  the  contact  points 


222  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

of  the  solutions  were  negligible.1  Under  such  circumstances  the  elec- 
tromotive force  as  previously  given,  for  a  cell  in  which  the  metal 
electrodes  dip  into  the  two  differently  concentrated  solutions  of  the 
salt,  is 


VQ        /\ 

This  equation  was  obtained  by  adding  the  potential-differences  exist- 
ing at  the  electrodes  —  that  is,  with  the  application  of  the  idea  of 
electrolytic  solution  pressure.  In  the  addition  the  solution  pres- 
sures were  cancelled  from  the  equation,  as  they  have  the  same  value 
for  the  two  similar  electrodes  and  are  oppositely  directed. 

It  was  also  found  possible  to  obtain  the  value  of  F,  without  any 
assumption  of  solution  pressure,  by  the  so-called  purely  energetic 
method.  It  was  only  necessary  to  take  into  account  the  condition 
of  the  system  before  and  after  the  passage  of  a  certain  quantity  of 
electricity,  without  attempting  to  understand  why  a  potential-differ- 
ence and  electric  current  are  manifested.  The  maximum  work 
obtainable  osmotically  by  the  change  of  the  system  from  its  original 
to  its  ultimate  state  is  calculated,  and  this  maximum  is  considered 
as  the  equivalent  of  the  electrical  energy  obtainable  from  the  process. 
The  values  of  F  calculated  in  both  ways  agreed  without  exception. 

It  remains  to  be  seen  whether,  when  a  potential-difference  occurs 
at  the  point  of  contact  of  the  liquids,  the  two  methods  of  calculation 
still  yield  the  same  result.  For  this  purpose,  the  following  concen- 
tration cell  is  selected  :  — 

Zinc  —  ZnCl2  solution,  concentrated  --------  • 

Zinc  —  ZnCl2  solution,  dilute  ----------------  !* 


1.  Calculation  of  F  by  means  of  the  electrolytic  solution  pressure. 

The  electromotive  force  of  the  cell  consists  of  three  potential- 
differences,  namely,  the  two  at  the  electrodes  and  that  at  the  point  of 
contact  between  the  two  liquids.  The  sum  of  the  first  two  is 


T> 

+  F2  =  F(1+2)  =  —  In  —  , 

where  P  and  P±  are  the  osmotic  pressures  of  the  zinc  ions  in  the  con- 
centrated and  dilute  solutions,  respectively,  the  corresponding  pres- 
sures of  the  chlorine  icns  being  2  P  and  2  Plt 

1  For  a  description  of  a  msans  for  attaining  this  end,  see  Ztschr.  phys.  Chem., 
14,  145  (1897). 


ELECTROMOTIVE  FORCE  228 

The    third   potential-difference    is  calculated  according   to   the 
formula  (6),  and  is 

~2~ 

F3=~ 


where  uc  and   ua  are  the  velocities  of  migration  of  the  zinc  and 
chlorine  ions.     The  sum  of  F(i+2)  and  F3  is 


__                       ug  —  2va\_      3u< 
Fa+2+3)  = m-=r  f  -r 


or  if  the  transportation  ratios  are  introduced,  na  = 2 — 

u«  +  ua 
and  1  —  na  •. 

and 


F3  must  be  subtracted  from  F(1+2)  as  indicated,  since  the  calculation 
of  F3  presupposes  the  direction  of  the  positive  current  from  the  con- 
centrated to  the  dilute  solution  within  the  cell,  while  with  F(1+2)  the 
current  passes  in  the  opposite  direction. 

2.  Calculation  of  F  by  means  of  the  principles  of  energetics.  The 
process  is  exactly  that  outlined  on  page  198.  If  2  Q  be  allowed  to 
pass  through  the  cell,  an  ion-mol  of  zinc  passes  into  the  dilute,  while 
the  same  quantity  is  deposited  from  the  concentrated,  solution.  In 
addition,  the  quantity  (1  —  na)  ion-mol  s  of  zinc  passes  from  the  dilute 
to  the  concentrated  solution,  (1  —  na)  being  the  transference  share  of 
the  zinc  ions.  The  dilute  solution  is  now  richer  by  na  ion-mols  of  zinc, 
while  the  concentrated  one  has  lost  this  amount.  Simultaneously, 
however,  an  amount  of  chlorine  ions  equivalent  to  the  na  zinc  ions 
has  also  passed  from  the  concentrated  to  the  dilute  solution  ;  conse- 
quently the  quantity  na  iort-rnols  of  zinc  and  its  equivalent  of  chlorine 
ions  have  been  moved  from  the  concentrated  to  the  dilute  solution. 
The  maximum  osmotic  work  corresponding  to  the  zinc  ions  is 


and  since  there  are  two  chlorine  ions  to  each  zinc  ion,  it  has  for  the 
chlorine  ions  the  value 


or,  added  together,  W=  3naHTln—. 

PI 


224  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

The  electrical  energy  is  2  FQ,  and  therefore 


which  is  the  same  as  the  equation  derived  above. 

This  agreement  in  the  methods  gives  also  a  method  for  determin- 
ing the  magnitude  of  potential-differences  at  the  contact  points  of 
liquids.  It  is  only  necessary  to  calculate,  as  above,  the  sum  of  the 
potential-differences  occurring  at  the  two  electrodes,  and  subtract  it 
from  the  actually  measured  electromotive  force  of  the  whole  cell,  to 
obtain  the  desired  value. 

Finally,  it  should  also  be  mentioned  that  the  electromotive  force 
of  concentration  cells  may  also  be  calculated  by  means  of  an  appli- 
cation of  the  principles  of  energetics  to  processes  other  than  the 
osmotic  process  used  in  this  book.  For  instance,  the  process  of 
isothermal  distillation,  first  used  by  Helmholtz,1  is  well  adapted  to 
the  calculation  of  the  eloctromotive  forces  of  concentration  cells. 
In  making  use  of  this  process,  a  knowledge  of  the  vapor  pressures  of 
the  differently  concentrated  solutions  is  essential. 

On  the  whole,  the  process  involving  osmotic  pressures  is  to  be 
preferred  in  the  case  of  dilute  solutions  because  the  requisite  knowl- 
edge of  the  osmotic  pressure,  or  the  proportional  concentration  of  the 
ions,  is  readily  available. 


GENERAL   CONSIDERATION   OF   CONCENTRATION  AND 
LIQUID  CELLS 

All  the  cells  thus  far  described  have  the  common  characteristic 
that  their  electrical  energy  is  not  generated  from  chemical  energy.  In 
every  case  there  was  simply  a  passage  of  material  from  a  higher 
to  a  lower  pressure,  and  whether  it  be  gas  or  a  dissolved  substance 
which  undergoes  this  change,  the  process  does  not  affect  the  internal 
energy.  The  work  done  does  not  therefore  come  from  the  internal 
energy,  but  is  derived  from  the  heat  of  the  surroundings.  Conse- 
quently the  galvanic  cells  thus  far  considered  are  really  machines  for 
transforming  the  heat  of  their  surroundings  into  electrical  energy. 

According  to  the  generally  applicable  formula  of  Helmholtz  (see 
page  173), 


1  Wied.  Ann.,  3,  201  (1878),  and  14,  61  (1881). 


ELECTROMOTIVE  FORCE  225 

In  the  present  case  Q,  the  heat  generated  by  the  chemical  reaction, 
is  zero  ;  therefore 


This,  on  integration,  gives 


T+koT^k. 


The  change  of  the  electromotive  force  of  these  cells  with  the  tem- 
perature is  determined  by  the  relation  existing  between  the  electro- 
motive force  and  the  corresponding  absolute  temperature.  The 
electromotive  force  itself  is  proportional  to  the  absolute  tempera- 
ture. When  in  activity,  the  cell  cools  itself  and  takes  up  heat  from 
the  surroundings. 

The  same  conclusions  are  reached  on  proceeding  in  still  another 
way.  The  electromotive  force  of  one  of  the  previously  mentioned 
concentration  or  liquid  cells  is,  in  general, 

£>  ;•,•:.   «•> 

from  which  ^=  x^  In  £.  (6) 

On  differentiation  with  respect  to  T 

^  _R1P  xv 

5r~    *      Pi 

T> 

is  obtained,  if  x  and  In—  for  "ideal"  solutions  are  considered  as 

P\ 

practically  independent  of  the  temperature. 
By  combination  of  (6)  and  (c), 


is  again  obtained. 

It  will  be  well  to  bear  in  mind  that  the  electromotive  force  is  only 
correctly  calculable  by  this  method  when  the  solutions  are  so  dilute 
that  the  laws  of  gases  are  applicable,  for  it  is  upon  this  assumption 
that  the  maximum  work  is  estimated.  As  a  matter  of  fact  solutions 
are  often  used  which,  on  being  mixed,  generate  considerable  quanti- 
ties of  heat,  and  are  therefore  far  from  being  ideal  solutions.  For 


226  A   TEXT-BOOK   OF   ELECTRO-CHEMISTRY 

such  solutions  the  Q  of  Helmholtz's  formula  is  evidently  not  zero, 
and  the  relation, 

F  _dv 

T~~dT 
no  longer  holds  good. 

It  is,  then,  to  be  noticed  that  the  Helmholtz  equation  in  its  above 
form  applies  only  when  the  chemical  process  resulting  from  the 
passage  of  a  definite  quantity  of  electricity  is  not  a  function  of  the 
temperature.  This  is,  however,  not  the  case  for  most  concentration 
or  liquid  cells,  since  the  transference  number  na,  and,  among  other 
properties,  also  the  valence  v,  is  a  function  of  the  temperature.  For 
this  reason,  the  quantity  x  which  appears  in  the  second  equation 
derived  cannot  be  considered  as  independent  of  the  temperature.  In 
agreement  with  these  considerations  it  is  found  that  the  electro- 
motive force  of  such  cells  in  general  is  not  at  all  proportional  to  the 
absolute  temperature. 

In  still  another  respect  the  application  of  the  Helmholtz  equation 
is  of  interest.  Generally  the  electromotive  force  of  a  cell  cannot,  as 
has  often  been  emphasized,  be  calculated  from  the  value  of  its  heat 
effect  alone.  In  the  following  case,  however,  the  electromotive  force 
can  be  so  calculated,  or,  more  strictly  speaking,  the  value  of 

dv 

dT' 

which,  together  with  the  value  of  Q,  must  be  known  in  order  to  cal- 
culate F,  may,  in  the  case  of  many  concentration  cells,  be  calculated 
directly  from  the  value  of  Q.  This  has  been  shown  by  van't  Hoff, 
Cohen,  and  Bredig.1 

Consider  the  concentration  cell, 


Hg,   Hg2S04,   solid,  —  NagSO^  saturated  ----  , 
Hg,  Hg2S04,  solid  -  Na2S04,  0.25  Cn-  -------  1' 

It  is  evident  that  the  electromotive  force  of  this  cell  will  be  equal 
to  zero  at  the  temperature  at  which  the  saturated  solution  of  sodium 
sulfate  is  0.25  normal.  If  at  this  temperature,  which  is  —  16.2°  t,  a 
current  be  allowed  to  pass  through  the  cell,  sodium  sulfate  goes 

1  Ztschr.  phys.  Chem.,  16,  453  (1895).     As  has  been  mentioned  by  Nernst, 
here  also  the  modified  Helmholtz  equation, 

Q<JF      Qvdna  _  FQ  —  Q 
~dT       nadT  ~       T 

must  be  used  because  of  the  variability  of  n«. 


ELECTROMOTIVE  FORCE  227 

into  solution  on  one  side  and  separates  on  the  other.  The  value  of 
Q  is  easily  calculated  from  the  heats  of  solution  and  dilution  of  the 
salt.  The  following  form  of  the  Helmholtz  equation  may  now  be 
applied :  — 


If  this  value  of  —  be  multiplied  by  16.2°,  the  preliminary  value" 

of  F  at  0°  t  is  obtained.     With  the  aid  of  this  value  and  the  exact 
value  of  Q  at  0°  t,  the  value  of 

(— \ 
\&TJ~* 

may  be  calculated.     If,  further,  the  average  of  the  two  values 

and  r-r~l 


be  multiplied  by  16.2,  a  more  accurate  value  of  F  at  zero  is  obtained. 
By  a  repetition  of  this  calculation  the  value  of  F  at  0°  t  becomes 
more  and  more  nearly  correct.  The  value  of  the  electromotive  force 
obtained  experimentally  agrees  well  with  the  value  calculated  in 
this  manner. 

It  is  especially  evident  from  this  example  that  it  is  not  in  harmony 
with  fact  to  consider  the  heat  of  solution,  or  of  dilution,  etc.,  exclu- 
sively as  the  source  of  the  electrical  energy,  for,  at  —16.2°  for 
example,  the  heat  of  solution  of  sodium  sulfate  is  very  great,  while 
the  electrical  energy  is  equal  to  zero.  On  the  other  hand,  there  is  a 
close  relation  between  the  temperature  coefficient  of  the  electro- 
motive force  and  the  heat  of  solution.  This  appears  accountable 
when  it  is  considered  that  the  heat  of  solution  is  closely  related  to 
the  temperature  coefficient  of  the  logarithm  of  the  concentration,  and 
that  the  electromotive  force  depends  upon  the  latter  value. 

In  the  concentration  cell, 

Hydrogen  in  platinum  black  —  alkali  solution , 

Hydrogen  in  platinum  black  —  acid  solution '' 


the  electromotive  force  depends  principally  upon  the  difference 
between  the  concentrations  of  the  hydrogen  ions  in  the  two  solutions. 
When  the  cell  is  in  operation,  the  neutralization  of  acid  and  base 
takes  place,  not  at  the  point  of  contact  of  the  two  solutions,  but  at 
the  electrodes.  The  electromotive  force  of  this  cell  can  be  calculated 


228  A  TEXT-BOOK  OF   ELECTRO-CHEMISTRY 

from  the  heat  effect  of  the  process,  i.e.  the  heat  of  neutralization, 
only  with  the  aid  of  its  temperature  coefficient. 

THERMOELECTRIC  CELLS  — THE  ELECTROMOTIVE  SERIES 

In  connection  with  the  foregoing  a  few  words  may  well  be  devoted 
to  thermoelectric  cells.  Heat  is  here  subjected  to  a  transformation 
into  electrical  energy  caused  by  a  difference  of  temperature.  On 
the  other  hand,  in  the  concentration  cells  heat  at  a  constant  tem- 
perature is  changed  into  electricity,  accompanied  by  the  simultaneous 
passage  of  a  substance  from  a  higher  to  a  lower  concentration.  This 
cannot  be  considered  as  contrary  to  the  second  law  of  thermody- 
namics, because,  according  to  this  law,  it  is  only  in  a  cyclical  process 
that  no  heat  at  constant  temperature  can  be  changed  into  work.  In 
other  processes  such  a  transformation  may  well  occur. 

The  potential-difference  at  one  electrode  may  be  expressed  by  the 
equation, 

RT,     P 

F  =  —  In  —  i 

VQ          P 

and  is  accordingly  proportional  to  the  absolute  temperature.  The 
arrangement 

Zn  —  ZnS04  solution,  —  Zn 

will  produce  no  electrical  energy  at  constant  temperature,  since  the 
two  potential-differences  of  such  a  cell  are  equal  and  oppositely 
directed.  But  if  one  of  the  contact  points  between  electrode  and 
solution  be  warmed,  the  corresponding  potential-difference  changes 
and  an  electric  current  is  produced.  As  the  potential-difference  at 
the  point  of  contact  between  two  solutions  is  also  proportional  to  the 
absolute  temperature,  it  is  immediately  clear  that  the  following 
cyclical  arrangement  should  produce  an  electric  current: 

Solution  <7j  at  2\  —  Solution  (72  at  Tv , 

Solution  Ci  at  T2  —  Solution  <72  at  T2 !' 


Here  Ci  and  C2  represent  the  concentrations  of  the  solutions. 
Since  the  osmotic  pressure,  the  solution  pressure,  and  transference 
numbers  are  functions  of  the  temperature,  the  electromotive  force  of 
a  thermoelectric  cell  cannot  be  calculated  in  a  simple  manner.  For 
further  considerations  of  this  point  the  reader  is  referred  to  the 
original  work  of  Nernst,1  in  which  this  theory  was  first  developed. 

Another  kind  of  thermoelectric  cell  is  that  discovered  by  Seebeck 

1  Ztschr.phys.  Chem.,  4,  169  (1889). 


ELECTROMOTIVE   FORCE  229 

in  the  year  1821,  in  which  only  conductors  of  the  first  class  enter. 
The  following  arrangement  represents  such  a  cell :  — 


First  metal  at  Tl  —  Second  metal  at  Tr 
First  metal  at  T2  —  Second  metal  at  T2 


These  cells  are  of  special  importance  since  by  means  of  them  the 
numerical  values  of  the  potential-differences  between  the  metals 
may  be  determined.  , 

Since  a  thermoelectric  cell  generates  an  electric  current  only  by 
the  change  of  heat  into  electrical  energy,  the  equation  given  on 
page  225  applies :  — 

L  =  dF.    F=:TdF_ 
T     dT*  dT' 

and  this  applies  equally  well  to  the  combination  as  a  whole  as  to 
the  individual  potential-differences,  since  a  cell  can  always  be  con- 
ceived in  which  there  exists  only  the  potential-difference  considered. 
It  is,  therefore,  only  necessary  to  know  the  change  of  the  potential- 
difference  with  the  temperature  ( — y  at  the  point  of  contact  be- 
tween two  metals,  in  order  to  be  able  to  calculate  F,  or  the  potential- 
dp 
difference  at  the  temperature  T.  The  value  of  —  may  be  directly 

obtained  from  the  electromotive  force  of  a  thermoelectric  cell  con- 
sisting of  the  two  metals  in  question,  the  temperature  at  one  contact 
point  being  T,  and  that  at  the  other  T-\-dT.  If  the  temperature 
T  is  common  throughout,  the  electromotive  force  is  zero,  as  the 
two  potential-differences  are  equal  and  opposite.  It  is  only  because 
one  of  the  potential-differences  may  be  changed  by  a  temperature 
change  that  the  electromotive  force  assumes  a  certain  value,  namely, 
that  of  the  alteration  in  the  potential-difference.  From  the  formula 
it  is  evident  that  if  dTis  unity,  the  electromotive  force  of  the  cell  is 
TdF. 

The  values  of  F,  calculated  for  pairs  consisting  of  the  most  widely 
differing  metals  at  the  ordinary  temperature,  are  very  small,  and 
amount,  even  in  exceptional  cases,  to  but  a  few  hundredths  of  a  volt. 
In  the  preparation  of  thermoelectric  piles  the  latter  metals  or  alloys 
are  especially  valuable.  A  notably  high  electromotive  force,  namely, 
from  0.2  to  0.3  of  a  voll^  results  from  the  combination, 

Copper  sulfide  —  Copper, 
if  the  point  of  contact  is  heated  to  about  500°  t. 


230  A  TEXT-BOOK  OF   ELECTRO-CHEMISTRY 

It  may  be  wondered  whether  or  not  it  would  be  possible  to  pro- 
duce electrical  energy  commercially  by  means  of  thermoelectric 
piles  instead  of  steam  engines.  In  each  case,  the  process  which 
furnishes  the  energy  is  the  passage  of  heat  from  a  higher  to  a  lower 
temperature.  The  maximum  efficiency  may,  in  each  case,  be  calcu- 
lated in  the  same  manner  with  the  aid  of  the  second  law  of  ener- 
getics. The  pile  equals  the  steam  engine  in  simplicity  and  excels 
it  especially  in  that  it  may  operate  through  a  greater  temperature 
difference.  As  a  matter  of  fact,  there  is  a  possibility  of  making 
such  a  change  from  the  steam  engine  to  the  thermoelectric  pile, 
even  if  at  present  it  is  not  feasible  because  of  the  expense  of  con- 
struction, of  the  great  loss  of  heat  by  conduction,  and  of  the  con- 
sumption of  a  part  of  the  electrical  energy  produced  (which  means 
that  the  quantity  of  work  obtainable  from  this  electrical  energy  is 
decreased)  in  overcoming  the  great  internal  resistance  of  the  pile. 
Furthermore,  recent  experiments  seem  to  indicate  that  the  problem 
of  transforming  heat  into  electrical  energy  in  this  manner  is  not  at 
all  hopeless.1 

The  results  of  the  calculations  of  the  electromotive  force  which 
have  been  carried  out  are  in  good  agreement  with  the  assumption, 
made  earlier,  that  the  chief  source  of  the  electromotive  force  of  a 
cell  i&  the  contact  surface  between  the  electrode  and  electrolyte. 
It  seems,  however,  upon  a  closer  consideration  of  actual  measure- 
ments, that  the  deduction  itself  is  not  satisfactory,  at  least  in  some 
cases;  for  the  measurements  show  that  the  electromotive  force  is 
not  always,  but  only  in  the  case  of  certain  metal  combinations  and 
within  narrow  temperature  limits,  proportional  to  the  absolute 
temperature. 

Many  thermoelectric  couples  show  so-called  reversal  points,  i.e. 
their  electromotive  forces  decrease  with  rising  temperature,  finally 
becoming  zero.  The  current  then  changes  its  direction.  Other 
processes  besides  those  assumed  must,  therefore,  take  place  at  the 
point  of  contact  of  the  two  metals. 

At  all  events,  there  is  no  reason  for  supposing  a  considerable 
potential-difference  to  exist  between  metals  ;  while,  on  the  contrary, 
the  existence  of  slight  potential-differences  has  been  shown  to  be 
probable. 

The  law  of  the  electromotive  series  must  evidently  apply  to  the 

minute  potential-differences  existing  between  the  metals  themselves. 

A  cell  composed  of  only  two  metals  cannot,  therefore,  generate  an 

electric  current   when  the   temperature   is   the   same  throughout. 

lZtschr.  fflektrochemie,  9,  91  (1903). 


ELECTROMOTIVE   FORCE  231 

This  conclusion  is  necessitated  by  the  second  law  of  energetics. 
Otherwise  any  desired  quantity  of  heat  at  constant  temperature 
could  be  changed  into  electrical  energy  without  any  permanent 
alteration  taking  place  in  the  system ;  which  is  equivalent  to  saying 
that  a  cyclical  process  may  continually  change  heat  into  work. 
That  this  electromotive  series  exists  does  not  explain  that  discov- 
ered by  Volta,  since  in  the  latter  the  forces  are  very  much  greater. 
Volta  thought  that  the  potential-difference  now  ascribed  to  the  sur- 
face between  liquid  and  metal  was  really  produced  at  the  contact 
point  between  the  metals.  To  corroborate  his  conclusions,  the  exist- 
ence of  a  similar  law  governing  the  potential-differences  at  the 
surface  between  metals  and  liquids  must  be  demonstrated. 

In  the  following  pages  it  will  be  seen  that,  theoretically,  a  certain 
definite  potential-difference  exists  between  a  metal  and  an  electrolyte. 
If,  for  example,  zinc,  in  contact  with  an  electrolyte  whose  potential 
is  zero,  exhibits  a  potential  of  3,  while  that  of  cadmium  is  2  and  of 
copper  1,  then,  according  to  the  electromotive  series,  the  potential- 
difference  between  zinc  and  copper  must  be  equal  to  the  sum  of  that 
between  zinc  and  cadmium  and  that  between  cadmium  and  copper. 
As  this  is  actually  the  case,  the  law  of  electromotive  series  may  be 
considered  correct. 

The  electromotive  series  is  roughly  applicable  to  galvanic  cells. 
The  arrangement, 

Zn  —  ZnS04  solution  —  CdSO4  solution \  ^ , 
Cu  -  CuS04  solution  —  CdS04  solution/     ' 

in  accordance  with  this  law,  should  exhibit  the  same  <ilectromotive 
force  as  the  arrangement, 


Zinc  —  zinc  sulfate  solution  --- 
Copper  —  copper  sulfate   solution 


if  the  concentrations  of  the  zinc  and  copper  sulfate  solutions  are 
the  same  in  both  cases.  This  is,  however,  only  exceptionally  the 
case.  Because  of  the  potential-differences  which  exist  in  most 
cases  at  the  point  of  contact  of  two  liquids,  the  law  is  only  approxi- 
mately true.  That  the  law  applies  to  simple  liquid  cells  only  in  a 
certain  definite  case,  has  already  been  mentioned. 

CHEMICAL  CELLS 

The  cells  thus  far  described,  in  which  the  electrodes  are  always  of 
the  same  nature,  may  in  most  cases  be  characterized  as  concentration 


232  A  TEXT-BOOK  OF   ELECTRO-CHEMISTRY 

cells.  To  be  distinguished  from  these  cells  are  those  in  which  the 
electrodes  are  different  and  in  which  chemical  energy  is  transformed 
into  electrical  energy.  They  may  be  called  chemical  cells.  A  type 
of  this  latter  class  is  the  well-known  Daniell  cell, 


Zinc  —  ZnS04  solution , 

Copper  —  CuS04  solution— 

When  in  activity,  zinc  passes  from  the  metallic  into  the  ionic,  and 
copper  from  the  ionic  into  the  metallic  state.  In  this  process  (in 
contradistinction  to  the  ideal  concentration  cells)  a  change  in  the 
internal  energy  of  the  system  takes  place,  and  this  difference  in 
energy  may  be  considered  as  the  principal  source  of  the  electrical 
energy  produced.  Instead  of  the  change  of  positive  ions  to  metal  at 
one  pole,  and  the  metal  to  ions  at  the  other,  the  negative  ions  may 
also  perform  this  process.  The  cell, 


Oxygen  (platinized  Pt)  —  KOH  solution- 
Chlorine  (platinized  Pt)  —  KC1  solution  -- 


causes  hydroxyl  ions  to  be  produced  in  the  alkali  solution  and 
chlorine  ions  to  change  into  molecular  chlorine  in  the  potassium 
chloride  solution.  (The  current  and  process  may  be  reversed  under 
certain  circumstances.) 

Finally,  positive  ions  may  form  at  one  electrode  simultaneously 
with  the  negative  ions  at  the  other.  An  example  is  seen  in  the 
combination, 


Zinc  —  ZnS04  solution 

Chlorine  (platinized  Pt)  —  KC1  solution- 


It  is  also  well  to  remember  that  in  all  such  cells  there  is  always  a 
small  potential-difference  produced  at  the  surface  of  contact  of  the 
solutions.  * 

As  already  noted,  the  electrical  energy  may  be  calculated  by  the 
Helmholtz  equation,  from  the  heat  generated  by  the  chemical  pro- 
cesses and  the  experimentally  determined  temperature  coefficients 
of  the  electromotive  force.  The  cell  during  activity  yields  as  elec- 
trical energy  the  maximum  work  obtainable  through  the  change 
which  takes  place  in  it.  This  work  bears  that  relation  to  the  heat 
of  the  chemical  reactions  measured  in  the  calorimeter  which  is  given 
by  the  Helmholtz  equation.  As  this  equation  shows,  there  may  be 
elements  in  which  the  chemical  or  internal  energy  change  is  exactly 
equal  to  the  electrical  energy  obtained.  These  may  be  considered 


ELECTROMOTIVE  FORCE  233 

as  machines  which,  in  their  action,  will  change  all  the  energy  put 
into  them  into  another  energy  form.  There  are,  secondly,  cells  in 
which  only  a  portion  of  the  chemical  energy  is  transformed  into 
electrical  energy,  and  these  may  be  looked  upon  as  machines  which 
transform  only  a  portion  of  the  energy  introduced  into  another  form 
of  available  energy,  while  the  remainder  is  lost  as  heat.  A  third 
kind  of  cell  is  also  known,  by  which  more  electrical  energy  is  pro- 
duced than  corresponds  to  the  chemical  reactions  taking  place,  and 
such  elements  may  be  considered  as  machines  transforming  not  only 
the  applied  energy  into  work,  but  absorbing  and  changing  into  work 
the  heat  of  the  surroundings.  Imagine  in  this  last  class  the  amount 
of  work  which  really  comes  from  the  heat  of  the  surroundings  con- 
tinually increased;  cells  are  finally  reached  in  which  (as  in  the 
concentration  cells)  the  internal  energy  remains  unaltered  and  the 
electrical  energy  is  derived  entirely  from  the  heat  of  the  surround- 
ings. It  then  becomes  a  question  whether  or  not  these  are  to  be 
designated  chemical  cells.  From  these  remarks  it  may  be  seen  that 
a  sharp  line  of  demarcation  between  the  chemical  and  other  cells 
does  not  exist,  but  one  form  gradually  passes  over  into  the  other. 
The  distinction  is  justifiable  in  so  far  as  the  chemical  reaction  is  the 
chief  characteristic  of  the  cells. 

The  influence  of  concentration  changes  in  the  electrolytes  of  any 
cell  upon  the  electromotive  force  may  be  predicted  from  the  princi- 
ples established  for  concentration  cells.  When,  for  example,  the 
Daniell  cell  is  in  operation,  zinc  ions  enter  the  zinc  sulfate  solution 
and  copper  ions  separate  out  from  the  copper  sulfate  solution.  If 
now  the  concentration  of  the  zinc  ions  be  increased,  it  is  evident 
that  zinc  ions  can  less  easily  enter  the  solution.  The  electromotive 
force  is,  therefore,  diminished.  If,  on  the  other  hand,  the  concen- 
tration of  the  copper  ions  be  increased,  the  deposition  of  copper  ions 
is  facilitated,  and  hence  the  electromotive  force  is  increased. 
Finally,  if  the  concentrations  of  the  ions  in  the  two  solutions 
are  changed  equally,  the  electromotive  force  remains  unchanged, 
since  the  effects  produced  at  the  two  electrodes  compensate  each 
other. 

In  general  the  rule  holds,  that  the  electromotive  force  of  a  cell  is 
decreased  when,  at  an  electrode,  the  solution  is  made  more  concen- 
trated in  respect  to  the  ions  which  this  electrode  sends  into  the 
solution  during  the  activity  of  the  cell.  On  the  other  hand,  the 
electromotive  force  is  increased  when  the  concentration  of  the  ion 
which  separates  at  the  electrode  is  increased.  For  example,  when 
both  solutions  of  the  cell, 


234  A   TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

Zinc  —  Zinc  sulfate  solution 

Chlorine  —  Hydrochloric  acid  solution 


are  diluted,  the  electromotive  force  is  increased. 

The  magnitude  of  the  change  of  the  potential-difference  or  of  the 
total  electromotive  force  may  be  calculated  directly  from  the  equation 
which  applies  to  concentration  cells :  — 

RT ,     P 

p  = In  — 

VQ        P1 

If,  for  example,  only  univalent  ions  are  involved  and  at  one  elec- 
trode the  ion  concentration  1  normal  is  replaced  by  the  ion  concen- 
tration 0.1  normal,  the  change  in  the  electromotive  force  is  equal 
to  0.0575  volt  at  17°  t  (see  page  200).  These  conclusions  have  been 
finely  confirmed  by  experiment. 

The  electromotive  force  of  a  cell,  as  already  emphasized,  is  always 
made  up  of  the  sum  of  at  least  two  separate  potential-differences, 
namely,  those  which  exist  at  the  points  of  contact  of  the  two  elec- 
trodes with  the  liquid  of  the  cell.  (In  a  similar  manner,  the  tem- 
perature coefficient  of  the  electromotive  force  of  the  cell,  — ,  is  the 

sum  of  the  temperature  coefficients  of  the  component  potential- 
differences.)  It  was  endeavored  for  a  long  time  to  find  a  means  of 
obtaining  a  knowledge  of  these  component,  or  single,  potential- 
differences.  The  results  of  this  endeavor  will  now  be  considered. 

DETERMINATION  OF   SINGLE   POTENTIAL-DIFFERENCES 

By  the  experimental  investigations  of  Lippmann  upon  the  rela- 
tion existing  between  the  surface  tension  of  mercury  in  sulfuric 
acid  and  the  potential-difference  at  the  point  of  contact,  the  meas- 
urement of  single  potential-differences  was  first  made  possible.  The 
principal  result  of  Lippmann's  research  was  expressed  by  him  as 
follows:  The  surface  tension  at  the  contact  surface  between  mercury 
and  dilute  sulfuric  acid  is  a  continuous  function  of  the  electromotive 
force  of  the  polarization  at  that  surface. 

Helmholtz  later  made  the  researches  of  Lippmann  better  under- 
stood by  an  application  of  the  theory  of  the  electrical  double-layer. 
If  mercury  be  brought  into  contact  with  a  liquid,  e.g.  dilute  sulfuric 
acid,  it  assumes  a  positive  electrical  charge.  This  may  be  explained 
by  assuming  that  the  electrolyte  contains  mercury  ions,  very  possi- 
bly from  the  dissolving  of  a  little  oxide,  which  may  be  present  on 
the  surface  of  even  the  purest  mercury.  The  work  of  Warburg  has 


ELECTROMOTIVE   FORCE  235 

also  shown  that  the  mercury  may  be  oxidized  by  the  oxygen  dis- 
solved in  the  liquid,  and  may  thus  enter  the  ionic  state.  Because 
of  its  very  low  solution  pressure  the  mercury  itself  is  positively 
charged  in  a  solution  even  when  it  contains  very  few  of  its  ions. 

At  all  events,  there  exists  at  the  surface  of  contact  of  the  mer- 
cury and  the  solution  a  certain  potential-difference  which  depends 
upon  the  concentration  of  the  mercury  ions  in  the  layer  of  solution 
directly  in  contact  with  the  mercury.  If  now  a  weak  current  of  low 
electromotive  force  be  sent  from  an  auxiliary  electrode  through  the 
solution  to  the  mercury,  mercury  is  deposited  and  the  concentration 
of  the  ions  is  decreased,  and  the  potential-difference  is  changed  by 
the  magnitude  of  the  primary  electromotive  force,  whereupon  the 
current  ceases  to  flow.  Since  the  ion  concentration  has  been  de- 
creased, the  positive  charge  of  the  mercury  has  decreased  and  the 
surface  tension  increased. 

This  is  the  result  of  the  mutual  repulsion  of  the-  quantities  of 
positive  electricity  on  the  surface  of  the  mercury  as  well  as  of  the 
negative  electricity  in  the  electrolyte,  with  the  consequent  expansion 
of  the  surface  in  opposition  to  the  surface  tension.  If  a  portion  of 
this  electricity  be  removed,  the  surface  tension  naturally  increases. 
By  continued  increase  of  the  primary  electromotive  force,  a  condition 
may  be  reached  in  which  the  electrical  double-layer  disappears  and 
the  surface  is  electrically  neutral.  Evidently  at  this  point  the 
surface  tension  has  reached  its  maximum  value.  The  potential- 
difference  between  the  mercury  and  the  liquid  is  now  zero,  and 
the  applied  electromotive  force  of  the  polarizing  current  is  exactly 
equal  and  opposed  to  the  single  potential  of  the  auxiliary  electrode, 
which  may  in  this  way  be  found.  If  still  more  negative  electricity 
be  introduced,  the  mercury  becomes  negatively  charged,  and  the 
attracted  positive  ions  of  the  solution  form  a  new  electrical  double- 
layer,  differing  from  the  former  only  in  the  relative  position  of  the 
two  kinds  of  electricity.  The  surface  tension  of  the  mercury  must 
now  decrease  with  increased  negative  charges  at  the  surface  because 
of  the  mutual  repulsion  of  the  quantities  of  electricity. 

The  execution  of  the  above  experiment  is  simple  in  principle ;  the 
difficulties  which  must  be  overcome  in  accurate  investigations  need 
not  be  discussed  here.  The  apparatus  shown  in  Figure  46 l  may 
be  used.  The  capillary  c,  as  well  as  the  greater  part  of  the  tube  A, 
attached  to  c  by  a  rubber  tube,  are  filled  with  mercury,  c  dips  into 
the  cup  B,  which  contains  a  little  mercury,  and  above  this  is  the  elec- 
trolyte. The  position  of  the  mercury  in  the  capillary  is  observed  by 
1  Ztschr.  phys.  Chem.,  15,  1  C1894V 


236 


A   TEXT-BOOK  OF   ELECTRO-CHEMISTRY 


means  of  a  microscope.  The  bulb  G,  which  contains  mercury,  per- 
mits of  the  application  of  desired  pressures  through  its  elevation 
and  depression ;  it  is  attached  to  the  manometer  M  by  a  rubber 
tube.  A  bent  glass  tube  D  leads  from  the  latter  to  A,  the  connec- 
tions being  made  with  short  pieces  of  rubber  tubing.  Paraffin  oil 
serves  as  the  liquid  of  the  manometer,  increasing  the  delicacy 
of  the  reading.  A  small  vessel,  as  shown  at  F,  containing  both 
paraffin  oil  and  mercury,  is  connected  to  the  apparatus  between 
the  manometer  and  rubber  tube.  P  is  an  arrangement  for  impress- 
ing any  desired  potential-difference  on  the  mercury  in  the  capillary 
tube. 


2n   C 


It  is  to  be  recalled  that  when  a  capillary  is  placed  in  water,  the 
latter  rises  to  a  level  above  that  of  the  surrounding  liquid,  as  it 
wets  the  surface  of  the  glass.  On  the  other  hand,  with  mercury  the 
level  in  the  capillary  is  below  that  of  the  surrounding  liquid,  and, 
if  the  surface  tension  be  increased,  sinks  still  lower,  that  is,  it 
moves  against  the  pressure  of  the  mass  of  mercury.  It  is  only  in 
this  way  that  a  diminution  of  the  surface,  the  result  of  increased 
surface  tension,  can  occur. 

If  now  a  certain  potential  from  the  source  of  electricity  P  be 
applied  to  the  mercury  in  the  capillary  c,  the  surface  tension  of  the 
mercury  increases  and  the  meniscus  begins  to  rise.  In  order  to  hold 
this  in  its  original  position,  a  certain  pressure  must  be  exerted  by 


ELECTROMOTIVE  FORCE  237 

means  of  the  manometer.  As  the  applied  potential-difference  is 
increased  the  necessary  pressure  also  increases,  until  at  a  certain 
potential-difference  a  maximum  in  the  pressure  is  observed,  which, 
on  further  increase  of  the  potential-difference,  again  diminishes. 
The  potential-difference  corresponding  to  the  maximum  pressure  is 
that  which  is  naturally  assumed  by  the  large  mercury  surface,  the 
auxiliary  electrode,  in  the  electrolyte  at  B. 

In  order  that  the  results  may  not  be  variable,  it  is  necessary  to 
add  some  mercury  salt  to  the  electrolyte,  that  this  may  have  a 
certain  concentration  of  mercury  ions  throughout,  since  the  potential- 
difference  at  the  surface  of  the  metallic  mercury  is  dependent  thereon. 
The  question  is  naturally  raised  :  Is  not  the  electrode  an  unpolarizable 
one  when  sufficient  mercury  ions  are  present,  i.e.  is  it  not  an  electrode 
the  potential-difference  of  which  remains  nearly  constant  during 
electrolysis  ?  In  answer,  attention  is  directed  to  the  following :  By 
adding  mercury  ions  to  the  liquid,  the  mass  of  mercury  in  B,  the 
auxiliary  electrode,  becomes  a  nearly  unpolarizable  electrode,  which 
maintains  the  same  potential-difference  towards  the  electrolyte,  no 
matter  what  other  potential-differences  are  inserted  at  P.  Because 
of  its  small  surface  the  metallic  mass  in  the  capillary  only  comes 
into  direct  contact  with  a  very  small  part  of  the  electrolyte.  Conse- 
quently, on  the  application  of  a  potential-difference,  only  very  few 
mercury  ions  pass  from  the  electrolyte  into  metallic  mercury,  and 
new  ions  can  diffuse  into  the  layer  at  the  surface  but  slowly ;  there- 
fore this  electrode  is  practically  polarizable.  Evidently,  the  relative 
extent  of  the  surfaces  of  mercury,  or,  better,  the  relative  density  of  the 
currents  at  the  two  mercury  surfaces,  plays  the  important  part.  What 
is  actually  measured  is  the  potential-difference  at  the  larger  mercury 
surface,  since  this  alone  is  constant.  When  the  two  quantities  of 
mercury  are  connected  by  a  conductor,  that  in  the  capillary  changes 
its  surface  tension  until  it  possesses  the  same  potential-difference 
as  the  lower  mass.  This  is  essential  to  the  equilibrium  which  the 
current  first  flowing  tends  to  establish.  This  is  particularly  evi- 
dent when  the  larger  electrode  is  an  amalgam  instead  of  pure  mer- 
cury. For  instance,  if  it  be  copper  amalgam  and  the  solution  above 
it  contains  a  copper  salt,  the  potential-difference  between  metal  and 
liquid  will  be  less  than  before,  since  the  amalgam  assumes  a  less 
positive  charge.  The  mercury  in  the  capillary  again  assumes  the 
potential  of  the  lower  electrode  when  the  two  are  connected,  and  on 
introducing  independent  potential-differences  a  lower  value  than 
with  pure  mercury  is  sufficient  to  bring  about  the  maximum  surface 
tension. 


238  A   TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

By  this  method  it  is  possible,  by  avoiding  the  potential-difference 
which  occurs  at  the  point  of  contact  of  the  two  liquids  by  a  suitable 
choice  of  electrolytes,  or  by  applying  a  calculated  correction  (see 
page  219)  for  this  potential-difference,  to  determine  the  single 
potential-difference, 

Mercury  —  Electrolyte, 

and,  further,  neglecting  the  potential-difference  between  the  two 
metals,  to  determine  any  potential-difference, 

Metal—  Liquid. 

The  method  of  procedure  is  as  follows:  The  potential-difference, 
for  example,  of 

Hg  -  HgCl  (solid)  in  KC1,  Cm 

is  first  determined.  The  value  found  is  0.56  volt,  when  the  electrode 
is  positively  charged.  This  combination,  or  electrode,  is  then 
connected  with  the  combination  of  which  the  potential-difference  is 
desired.  Supposing  the  potential-difference 

Ag  -  AgN03,  Cn, 
to  be  desired,  the  electromotive  force  of  the  combination, 

Hg-HgCl  (solid)  in  KC1  solution,  Cn  _____  , 
Ag  -  AgN03  solution,  Cn  __________________  !' 

would  be  measured.  If,  from  this  value,  the  potential-difference 
between  mercury  and  potassium  chloride  solution  (0.56  volt)  be 
subtracted,  the  required  value  is  obtained. 

In  this  connection,  the  investigations  of  Bothinund1  with  the 
Lippmann  method  are  of  interest.  Instead  of  mercury,  he  used 
amalgams  of  the  base  metals,  which  even  at  a  concentration  of  about 
0.01  per  cent  exhibit  the  potential  of  the  pure  metal.  He  measured 
the  potential-differences  of  the  combinations, 


Pb  amalgam  -  ILjSO^  Cn,  sat.  with  PbS04  -  , 
Cu  amalgam  —  H2S04,  Cn,  -f  CuSO4,  0.01  Cm  -  , 
Hg  -  H2S04,  Cnt  sat.  with  Hg2S04  -  , 

and  also  of  the  cells  formed  by  connecting  the  latter  combination 
with  the  others  in  succession.  He  then  compared  the  latter  values 
with  the  sum  of  the  corresponding  single  potential-differences.  The 
values  obtained  are  given  in  the  following  table  :  — 

^Ztschr.  phys.  Chem.,  15,  1  (1894). 


ELECTROMOTIVE  FORCE  239 


AMALGAMS 

ELECTROLYTE 

SINGLE  POTENT.  -D  IFF. 

Copper 
Mercury 
Lead 

H2S04  (1  On)  +  CuS04,  0.01  <7n, 
H2SO4  (1  On)  saturated  with  Hg2S04 
H2SO4  (1  Cn)  saturated  with  PbSO4 

0.446  volt 
0.926  volt 
0.008  volt 

The  electrodes  were  positively,  and  the  electrolyte  negatively, 
charged. 

According  to  the  above  values,  the  electromotive  force  of  the 

Copper  —  Mercury  cell  =  0.481  volt, 
and  of  the  Lead  —  Mercury  cell  =  0.918  volt. 

The  values  actually  measured  are  0.458  and  0.923  volt,  respectively. 
In  other  cases  the  agreement  between  the  value  of  the  electromotive 
force  taken  as  the  sum  of  the  two  single  potential-differences  and 
that  actually  measured  was  less  satisfactory. 

To  sum  up,  the  following  should  be  noted:  The  theory  which 
has  been  outlined  is  based  on  the  supposition  that  the  surface  ten- 
sion of  the  mercury  is  related  to  the  electrical  double-layer  at  its 
surface  only  in  the  way  already  described,  and  especially  that  the 
nature  of  the  ions  forming  one  side  of  the  double-layer,  as  well  as 
the  nature  of  the  electrolyte  in  the  general,  is  without  influence  upon 
the  surface  tension  of  the  mercury.  Since,  however,  according  to 
recent  investigations  of  Nernst,  the  surface  tension  of  the  mercury, 
in  contradiction  to  the  theory,  is  strongly  influenced  by  nonelec- 
trolytes,  the  theory  and  therewith  the  significance  of  the  experi- 
mental results  is  rendered  uncertain.  Furthermore  Billitzer,1 
together  with  other  objections  to  the  theory,  has  called  attention 
to  the  fact  that  the  electrolytic  solution  pressure  of  mercury  must 
not  be  considered  as  a  constant,  but  as  a  variable  increasing  with  the 
surface  tension. 

There  is  a  second  method  which  can  be  used  for  the  determina- 
tion of  single  potential-differences,  the  principle  of  which  was  ex- 
plained by  Helmholtz.  Ostwald 2  first  showed  that  it  could  be  used 
for  this  purpose,  and  through  his  efforts,  as  well  as  those  of  Paschen, 
the  method  has  been  developed. 

If  an  insulated  mass  of  mercury  be  allowed  to  flow  in  a  stream 
through  a  fine  opening  and  drop  into  an  electrolyte,  there  oan  be, 
according  to  Helmholtz,  no  potential-difference  between  the  mercury 

1  Ztschr.  phys.  Chem.,  48,  513  (1904),  and  51,  166  (1905). 

2  Ztschr.  phys.  Chem.,  1,  583  (1887). 


240 


A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 


and  the  electrolyte.     Helmholtz  expressed  himself  on  this  point  in 
the  following  manner  :  — 

"  Consequently  I  conclude  that  when  a  quantity  of  mercury  is  con- 
nected with  an  electrolyte  by  a  rapidly  dropping  fine  stream  of  the 
mercury,  and  is  otherwise  insulated,  the  two  cannot  possess  different 
electrical  potentials,  for  if  a  potential-difference  did  exist,  for 
example,  if  the  mercury  were  positive,  each  falling  drop  would  form 
an  electrical  double-layer  on  its  surface,  requiring  the  removal  of 
positive  electricity  from  the  mass,  and  diminishing  its  positive 
charge  until  that  of  the  mercury  and  solution  reached  equality." 

An  experiment  by  A.  Konig  has  already  shown  that  the  charge  on 
the  mercury  can  be  partly  removed  by  allowing  it  to  drop  through 

a  solution.  This  result  was  later  con- 
firmed in  other  ways.  Figure  47  repre- 
sents the  arrangement  employed  by  Ko- 
nig. The  mercury  cup  a,  beneath  dilute 
sulfuric  acid,  was  connected  by  a  wire 
with  mercury  dropping  from  the  capillary 
into  the  acid.  A  galvanometer  G-  was 
connected  into  the  circuit  as  shown.  This 
indicated  that  the  positive  electricity  was 
removed  with  the  dropping  of  the  mer- 
cury in  agreement  with  the  previous  ex- 
planations. If  the  upper  mercury,  through 
the  dropping,  be  brought  to  practically 
the  same  potential  as  the  solution,  the 
polarizable  mercury  in  the  cup  has  the  same  potential,  and  therefore 
the  maximum  surface  tension.  This  could  be  determined  by  means 
of  an  ophthalmometer.  As  still  further  proof,  a  weak  electromotive 
force,  positive  or  negative,  on  being  introduced  into  the  circuit  on 
the  wire  connecting  the  two  electrodes,  caused  the  surface  tension  to 
decrease,  since  a  potential-difference  was  produced  between  the 
liquid  and  the  mercury  of  the  cup. 

According  to  the  Nernst  osmotic  theory,  the  following  statements 
concerning  the  drop  electrode  may  be  made : l  If  a  fine  stream  of 
mercury  be  allowed  to  flow  out  of  a  tube  into  a  solution  of  an  elec- 
trolyte containing  some  mercury  salt,  as  for  example  mercurous 
chloride,  mercury  ions  deposit  on  the  fresh  surface  of  the  mercury, 
each  drop  becomes  positively  charged  and  surrounded  by  the  nega- 
tive chlorine  ions  corresponding  to  the  ions  deposited.  Arriving  at 
the  bottom,  it  joins  the  constant  mercury  surface  there  and  gives  up 
1  Ztschr.phys.  Chem.,  25,  265  (1898),  and  28,  257  (1899). 


FIG.  47 


ELECTROMOTIVE   FORCE  241 

the  excess  of  its  positive  charge  by  sending  mercurous  ions  into  the 
solution.  These  ions,  with  the  chlorine  ions,  which  up  to  this  time 
constituted  the  outer  part  of  the  double-layer,  form  mercurous 
chloride  again.  As  a  result  of  this  process,  the  mercury  salt  is 
transferred  from  the  upper  to  the  lower  part  of  the  solution,  thus 
forming  a  concentration  cell.  Since  the  solution  becomes  more  con- 
centrated below  than  above,  it  would  be  expected  that  the  current 
would  flow  through  the  solution  from  the  upper  to  the  lower  part. 
This  is  actually  the  case.  Furthermore,  it  may  be  stated  that  the 
concentration  of  the  mercury  ions  in  the  upper  part  of  the  solution 
must  finally  become  so  small,  if  no  diffusion  takes  place,  that  the 
potential-difference  there  will  be  zero.  This  state  is  not  changed 
nor  is  there  a  further  transference  of  salt  from  the  upper  to  the 
lower  part  of  the  solution  when  more  mercury  is  allowed  to  drop 
through  the  solution. 

The  end  sought  has,  then,  been  attained;  for  by  throwing  an 
electromotive  force  into  the  circuit,  the  potential-difference  of  the 
lower  mercury  electrode  can  be  measured. 

As  a  matter  of  fact,  however,  the  presence  of  diffusion  prevents 
a  complete  freedom  of  electric  charge,  and  thus  causes  the  measure- 
ments to  be  both  difficult  and  uncertain.  However,  all  errors 
arising  from  the  fact  that  an  electric  charge  is  still  present  may  be 
avoided  by  a  method  recently  proposed  by  Nernst.  It  depends  on 
the  preparation  of  a  solution  of  so  small  a  concentration  of  mercury 
ions  that  the  potential-difference  between  it  and  a  mercury  surface  is 
equal  to  zero.  A  means  of  preparing  such  a  solution  is  offered  by 
potassium  cyanide.  It  has  been  found  that  in  a  concentrated  solu- 
tion of  potassium  cyanide,  the  direction  of  the  current  is  reversed, 
i.e.  it  flows  from  the  stationary  mercury  through  the  solution  to  the 
mercury  drops.  If  now  a  solution  of  potassium  cyanide  of  such  a 
concentration  be  prepared  that  no  electric  current  is  produced  when 
mercury  is  allowed  to  drop  through  it,  the  desired  zero  electrode  is 
obtained.  Experimental  results  obtained  by  Palmaer1  have  con- 
firmed the  correctness  of  this  conclusion.  With  the  use  of  a  zero 
electrode  made  as  above  described,  he  obtained  nearly  the  same  value 
for  the  single  potential-difference, 

Hg  -  KC1,  0.1  <7n,  saturated  with  Hg2Cl2, 

as  he  did  with  the  aid  of  the  capillary  electrical  method. 

In  view  of  this  work,  it  might  with  good  reason  have  been  thought 

1Ztschr.  Elektrochem.,  9,  754  (1903). 


242  A   TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

that  the  values  so  found  although  questioned  are  yet  near  the  correct 
one.1  The  recently  published  investigations  of  Billitzer,2  however, 
which  lead  to  entirely  different  values,  diminished  even  more  the 
probable  correctness  of  the  values  obtained  by  the  above  methods. 

As  has  already  been  explained  in  Chapter  VI,  at  the  surface  of 
contact  of  a  solid  and  a  liquid  there  is  always  formed,  according  to 
Helrnholtz,  an  electrical  double-layer.  Hence  an  electrically  charged 
particle  which  is  suspended  in  an  electrolyte  through  which  an  elec- 
tric current  is  flowing,  will,  according  to  the  nature  of  its  charge, 
migrate  toward  the  positive  or  toward  the  negative  pole.  If  all 
other  influences  which  also  may  cause  the  particle  to  move  be 
excluded,  then  the  sign  of  the  charge  upon  the  particle  may  be 
known  from  the  migration  direction  of  the  particle,  and,  further,  it 
may  be  concluded  that  at  that  point  at  which  the  direction  of 
migration  is  reversed,  i.e.  the  point  at  which  the  double-layer 
disappears,  a  system  of  two  bodies  with  a  potential-difference 
between  them  equal  to  zero  exists.  If  the  solid  particle  is  a  metal, 
the  system  is  a  zero  electrode  which  may  be  used  directly  for 
the  determination  of  the  single  potential-difference  of  any  other 
electrode  and  its  solution. 

The  investigations  were  carried  out  with  colloidal  platinum,  silver, 
and  mercury,  and  also  with  fine  metallic  wires  with  one  end  fused 
forming  a  small  sphere,  which  were  suspended  perpendicularly  from 
a  quartz  thread.  The  movement  took  place  and  the  reversal  could 
in  every  case  be  brought  about  by  changing  the  ion  concentration,  in 
agreement  with  the  Nernst  equation  relating  to  the  potential-differ- 
ence between  a  metal  and  its  solution.  The  same  results  were 
obtained  by  reversing  the  experiments.  When  metallic  powder  was 
allowed  to  fall  through  a  tube  containing  a  solution,  an  electric  cur- 
rent was  obtained.  The  direction  of  this  current  could  be  changed 
by  changing  the  ion  concentration  of  the  solution.  At  a  definite 
concentration,  by  the  first  method  the  particles  or  wires  ceased 
to  move,  and  by  the  second  method  the  electric  current  ceased  to 
flow. 

It  is  very  remarkable  that  the  value  of  the  potential-difference  of 
the  mercury  electrode  in  contact  with  a  normal  solution  of  potassium 
chloride  saturated  with  mercurous  chloride,  as  measured  by  the 
method  just  described,  differs  from  that  obtained  by  the  surface  ten- 
sion method  by  not  less  than  0.74  volt.  Since,  however,  the  value 

1  See  also  Kriiger,  "  Theorie  d.  Elektrokapill.  und  d.  Tropfelektr.,"  Getting. 
Ges.  d.  Wiss.,  1904,' Vol.  1. 

2  Ztschr.  Elektrochem.,  8,  638  (1902),  and  loc.  cit. 


ELECTROMOTIVE   FORCE 

obtained  by  the  new  method  may  contain  errors,1  Nernst2  has 
repeated  his  recommendation  that  until  the  subject  is  further  inves- 
tigated, the  value  at  present  usually  given,  i.e.  for  the  mercury 
electrode, 

?Hg- solution  =    +0.56  VOlt, 

be  disregarded,  and  that  the  potential-difference  of  the  hydrogen 
electrode  with  hydrogen  at  atmospheric  pressure  and  hydrogen  ions 
at  one  normal  concentration,  placed  arbitrarily  equal  to  zero,  be  taken 
as  a  standard.  It  should  especially  be  noted  that  up  to  the  present  no 
special  significance  has  been  attached  to  the  absolute  zero  point  of 
the  electrode  potentials.  Not  to  the  slightest  degree  has  it  a  signifi- 
cance such  as  that  which  the  absolute  zero  point  of  the  temperature 
scale  possesses ;  for  it  has  not  been  found  possible  to  find  a  numeri- 
cal relationship  between  solution  pressure  and  other  physical  proper- 
ties. Hence,  from  this  point  of  view,  no  objection  can  be  raised  to 
the  choice  of  an  arbitrary  zero  point,  i.e.  an  arbitrary  zero  electrode. 
The  choice  of  the  hydrogen  electrode  as  such  a  zero  electrode 
possesses  advantages  in  the  direction  of  systematization,  since  a 
division  of  the  metals  into  those  which  do,  and  those  which  do  not, 
evolve  hydrogen  is  thereby  effected.  On  the  one  side  there  are  the 
metals  which  are  less,  and  on  the  other  side  those  which  are  more, 
negative  than  hydrogen,  if  the  metals  be  considered  to  be  in  contact 
with  their  respective  normal  solutions.  Finally,  hydrogen  is  the  best 
reducing  agent,  and  in  this  respect  also  divides  the  electrodes  into 
two  classes. 

A  hydrogen  electrode  of  sufficient  constancy  for  general  use  is 
easily  prepared.  It  is  only  necessary  to  place  a  well-platinized 
platinum  electrode  into  a  sulfuric  acid  solution  which  is  normal  in 
respect  to  hydrogen  ions,  and  to  pass  a  stream  of  hydrogen  into  the 
solution,  and  past  the  electrode  for  fifteen  minutes,  in  order  to  obtain 
the  correct  potential-difference  within  0.001  of  a  volt.  The  deter- 
mination of  single  potential-differences  and  their  signs  is  then  in  the 
main  very  simple,  if  the  potential-difference  which  always  exists  at 
the  place  of  contact  of  the  two  liquids  be  left  out  of  consideration. 
The  electrode  which  is  to  be  investigated  is  connected  with  the  above 
standard  or  normal  hydrogen  electrode,  and  the  electromotive  force 
of  the  cell  thus  formed  and  the  direction  of  the  electric  current  in  the 
cell  are  determined  according  to  the  usual  methods.  This  electro- 

1  Ztschr.  Elektrochem.,  12,  192  and  281  (1906). 

2  Ztschr.  Elektrochem.,  7,  253  (1900)  ;  Ztschr.  phys.  Chem.,  35,  291  (1900) 
and  36,  91  (1901). 


244  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

motive  force  is  directly  the  value  of  the  single  potential-difference 
desired,  and  its  sign  is  plus  or  minus  according  as  the  electrode  in 
question  is  the  positive  or  the  negative  pole  of  the  cell.  The 
direction  of  the  current  is  represented  by  an  arrow. 

What  has  just  been  stated  is  illustrated  by  the  following  example. 
If  the  electromotive  force  of  the  cell 

Zn  -  Zn",  I  Cm  -  H",  1  Cn  -  H2 

is  equal  to  0.770  volt,  and  the  electric  current  flows  from  the  zinc 
electrode  through  the  solution  to  the  hydrogen  electrode,  then  the 
single  potential-difference  between  the  zinc  and  the  solution  of  zinc 
ions  is  equal  to  —  0.770  volt.  Representing  single  potential-differ- 
ence by  F  as  will  be  done  from  now  on,  this  may  be  expressed  as 
follows  :  — 

£zn  ->  solution  =  ~  0.770, 

or  F  80lution  +_  Zn  =  +  0.770  volt. 

The  sign  plus  or  minus  is  always  that  of  the  electrical  charge  of  the 
first-mentioned  component  in  the  equation,  i.e.  in  the  former  equa- 
tion, the  sign  of  the  electrical  charge  of  the  zinc,  and  in  the  latter, 
that  of  the  solution  of  zinc  ions. 

In  the  manner  just  illustrated,  any  single  potential-difference  may 
be  determined.  Moreover,  the  electromotive  force  of  a  cell  com- 
posed of  any  two  electrode  combinations  may  be  obtained  by  taking 
the  sum  of  the  single  potential-differences  of  these  combinations.  It 
should  be  noted  that  the  direction  of  the  arrow  in  the  case  of  single 
potential-differences  is  always  that  of  the  current  when  the  electrode 
combination  under  consideration  is  connected  with  the  normal 
hydrogen  electrode.  If  now  the  two  single  potential-differences 
composing  a  cell  be  written  one  after  the  other  in  the  order  in  which 
they  are  combined  in  the  cell,  and  if  the  two  arrows  have  the  same 
direction,  then  their  signs  are  the  same.  If  the  arrows  have  opposite 
directions,  the  signs  are  unlike.  In  the  latter  case,  the  direction  of 
the  current  in  the  cell  is  that  of  the  larger  single  potential-difference. 
This  is  illustrated  by  the  following  equations:  — 

(1)  FZn  ->•  sol.  4-  F80i.  _».  Cu   =  FZn  ->  Cu  9 

-0.770        -0.329        -1.099 


cu<—  sol.     ~       sol.  <—  Zn  Cu-«—  Zn 

+  1.099 

J?Zn  —  >  sol.  +  F  sol.  <—  Cd  =  F  Zn  —  >  Cd  ) 

-0.770         +0.420         -0.350 


ELECTROMOTIVE  FORCE  245 


Cd  —  >  sol.  sol.  «<—  Zn  =  FCd  <—  Zn- 

-0.420        +  0.770         +  0.350 
Hence  it  makes  no  difference  whether  we  write 

F  Zn  ->  cd  =  -  0.350,  or  F  Cd  ^_  Zn  =  +  0.350. 

In  either  case  the  meaning  is  the  same  and  the  arrow  shows  the 
direction  of  the  current  in  the  couple,  i.e.  from  one  electrode  through 
the  liquid  to  the  other.  In  the  case  represented  by  the  latter  equa- 
tions, the  current  flows  from  the  zinc,  the  negative  pole,  through  the 
liquid  to  the  cadmium,  the  positive  pole. 

This  method  of  representation  is  employed  in  exactly  the  same 
way  in  the  case  of  electrodes  which  send  negative  ions  into  the  solu- 
tion, such  as  oxygen,  chlorine,  bromine,  etc.,  electrodes.  When 
these  electrodes  are  in  combination  with  the  hydrogen  electrode,  the 
single  potential  difference, 

?  electrode  -liquid? 

receives  the  positive  sign  when  negative  ions  are  formed,  and  the 
negative  when  they  are  discharged.  By  means  of  this  method  of 
representation,  which  was  in  principle  suggested  by  Luther,  the  sur- 
vey and  comprehension  of  the  subject  has  been  greatly  facilitated. 
It  should,  however,  be  noted  that  it  is  not  in  general  use  in  electro-chemi- 
cal literature. 

Although  the  hydrogen  electrode  possesses  certain  advantages  as 
a  standard  electrode,  it  is  not  always  to  be  recommended  for  general 
use  in  the  measurement  of  single  potential-differences.  When  used 
in  carrying  out  measurements  with  neutral  or  very  concentrated 
alkaline  solutions,  diffusion  potential-differences  of  considerable 
magnitude  arise,  due  to  the  great  difference  in  the  migration  veloci- 
ties of  the  ions,  which  can  be  calculated  only  with  difficulty  if  at  all. 
In  such  cases  the  so-called  calomel  electrode,  which  is  very  constant 
and  easily  duplicated,  possesses  advantages  over  the  hydrogen 
electrode.1 

A  form  of  the  calomel  electrode  such  as  is  shown  in  Figure  48  may 
be  prepared  in  the  following  manner  :  2  At  the  bottom  of  a  small 
upright  vessel,  about  eight  centimeters  in  height  and  from  two  to 
three  centimeters  in  diameter,  a  small  quantity  of  pure  mercury  is 
placed  and  then  covered  with  a  layer  of  mercurous  chloride.  The 

1  See  also  the  discussion,  "  Ueber  die  Zahlung  der  Elektrodenpotentiale," 
Ztschr.  Elektrochem.,  11,  777  (1905). 

2  For    further    particulars   see    Ostwald-Luther,     Physik-chem.    Messungen, 
page  381 


246 


A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 


vessel  is  then  filled  with,  a  normal  solution  of  potassium  chloride  and 
closed  with  a  rubber  stopper  carrying  two  glass  tubes.  Through  one 
of  the  latter,  a  platinum  wire  is  connected  with  the  mercury.  The 
other  tube,  bent  as  shown  in  the  figure,  is,  together  with  the  rubber 

tube  attached  to  it,  filled  with  the 
solution  of  potassium  chloride. 
The  bent  glass  tube  B  of  the  calo- 
mel electrode  thus  made,  is  dipped 
into  the  liquid  of  the  electrode 
combination  the  potential-differ- 
ence of  which  is  desired,  and  the 
electromotive  force  of  the  cell 
thus  formed  is  measured  as  usual. 
If  the  potassium  chloride  solution 
produces  a  precipitate  with  the 
solution  of  the  electrode  combina- 
tion under  consideration,  as  would 
be  the  case,  for  example,  if  the 
latter  contained  a  solution  of  sil- 
ver nitrate,  a  third  and  indifferent 
solution,  e.g.  of  potassium  or  am- 
monium nitrate,  must  be  intro- 
duced between  them.  It  is  often 

advantageous  to  use  a  solution  of  potassium  chloride  because,  since 
the  migration  velocities  of  the  respective  ions  are  nearly  the  same, 
there  is  no  tendency  to  form  a  large  potential-difference  at  the  place 
where  the  two  solutions  meet.  Since  the  value  of  this  potential- 
difference  cannot  always  'be  calculated  with  certainty,  it  is  a  disa- 
greeable factor  in  the  measurement  of  single  potential-differences. 
In  the  case  of  a  contact  between  a  solution  of  potassium  chloride 
and  one  of  a  neutral  salt,  however,  its  value  is  sufficiently  small  to 
be  neglected.  Even  when  it  cannot  be  neglected,  it  may  easily  be 
made  calculable.1 

It  was  recommended  by  the  International  Congress  at  Berlin2  that 
in  all  cases  the  directly  measured  values  be  given,  and  that  the  1 
normal  calomel,  or  the  above-defined  Nernst  hydrogen,  electrode  be 
employed  as  the  auxiliary  electrode.  Following  these  recommenda- 
tions, the  correct  measured  values  will  always  be  available  for 
possible  future  recalculation.  These  values  may  be  considered  as 
single  potential-differences  referred  to  the  hydrogen  or  the  calomel 

1  Sammet,  Ztschr.  phys.  Chem.,  53,  668  (1905). 

2  Ztschr.  Electrochem.,  9,  686  (1903). 


FIG.  48 


ELECTROMOTIVE   FORCE  247 

electrode  as  a  zero  electrode.  In  this  case  it  must  be  borne  in  mind 
that  these  values  still  include  the  potential-differences  which  exist 
at  the  point  of  contact  of  the  two  solutions. 

In  the  following  table  are  given  the  most  reliable  values  of  the 
single  potential-differences, 

IT  electrode  -  electrolyte  > 

when,  at  room  temperature,  the  electrodes  are  in  contact  with  their 
respective  solutions  containing  one  ion-mol  per  liter. l  The  ion  con- 
centration is  in  many  cases  still  uncertain.2 

In  column  I  are  given  the  calculated  or  measured  single  potential- 
differences  against  the  calomel  electrode.  These  values  will  be 
represented  by  FC. 

In  column  II  are  given  the  calculated  or  measured  values  against 
the  hydrogen  electrode.  They  will  be  represented  by  FA. 

The  values  inclosed  in  parentheses  have  been  calculated  solely 
from  heat  effects. 

Since  the  potential-difference  between  the  calomel  and  the  hydro- 
gen electrode  is  equal  to  0.283  volt,  and  since  in  this  combination 
the  current  flows  from  the  hydrogen  electrode  through  the  solution 
to  the  mercury,  the  following  relation  exists, 


electrolyte 


+  0.283, 


when  the  calomel  electrode  is  referred  to  the  hydrogen  electrode  as 
zero  electrode;  and 

FH-^- electrolyte  =  ~  0.283, 

when  the  hydrogen  electrode  is  referred  to  the  calomel  electrode  as 
zero  electrode.  Hence  we  have  the  following  relation  between  the 
values  referred  to  these  two  standard  zero  electrodes,  — 

£ h  =  FC  +  0.283  volt. 

This  series  may  at  least  be  considered  as  the  approximately  cor- 
rect electromotive  series.  The  values  are  often  called  "electrolytic 
potentials"  and  represented  by  the  letters  (EP)  when  they  refer  to 

1  Wilsmore,  loc.  cit.    The  values  for  Fe,  Co,  and  Ni  were  obtained  from  the 
work  of  Muthmann  and  Fraunberger,  "  Math.-phys.  Kl.  d.  K.  Bayr.  Ak.  d.  W. 
34,"  Vol.  2  (1904)  ;  those  for  Ag  and  O  under  atmospheric  pressure  against  1 
normal  OH' from  an  investigation  of  Lewis,  Ztschr.  phys.  Chem.,  55,  473  (1906); 
and  those  for  Cl,  Br,  and  I  from  an  investigation  of  Luther  and    Sammet, 
Xfxchr.  Elektrochem.,  11,  295  (1905).   The  latter  values  were  obtained  by  extra- 
polation and  are  referred  to  a  halogen  concentration  of  one  mol  per  liter. 

2  Abegg-Labendzinski,  Ztschr.  Elektrochem.,  10,  77  (1904). 


248  A   TEXT-BOOK  OP  ELECTRO-CHEMISTRY 

ELECTROLYTIC  SINGLE  POTENTIAL-DIFFERENCES 


ELEMENTS 

KFC) 

li  (pA) 

(  -  3.48) 

(-3.20) 

(-3.10) 

(-2.82) 

(-3.10) 

(-2.82) 

Strontium     

(-3.05) 

(-2.77) 

Calcium    

(-2.84) 

(-2.56) 

Magnesium    

(-2.82) 

(-2.54) 

-  1.774  ? 

-1.491? 

-1.559? 

-1.276? 

Manganese    "  •'* 

-  1.358 

-1.075 

Zinc     ...     

-  1.053 

-0  770 

Cadmium       .          .... 

-  0.703 

-0420 

Iron      

-  0.940  1 

-0.6601 

Thallium  

-  0.605 

-0.322 

Cobalt  

-  0.730  1 

-  0.450  1 

Nickel  

-  0.880  1 

-  0.600  l 

Tin  

<  -  0.475 

<-  0.192 

Lead    

-  0.431 

-0.148 

Hydrogen  

-  0.283 

±  0.000 

Copper 

-f  0.046 

+  0.329 

<  +  0.010 

<  +  0.293 

Bismuth    

<  +  0.108 

<  +0.391 

Antimony           .          .          .... 

<  +  0.183 

<  +  0.466 

Mercury   .          

+  0.467 

+  0.750 

Silver   

+  0.515 

+  0.798 

Palladium     

<  +  0.506 

<  +  0.789 

Platinum  

<  +  0.580 

<  +  0.863 

Gold     

<  +  0.796 

<  +  1.079 

(+1.68) 

(  +  1.96) 

Chlorine  ^           (  «•    . 

+  1.120 

+  1.400 

Bromine  f  25°  •<   . 

+  0.812 

+  1.095 

Iodine      J           1       

+  0345 

+  0.628 

Oxvffen 

+  0.110 

+  0.393 

room  temperature.    According  to  the  Nernst  equation  (see  page  183), 
for  a  metallic  electrode, 


VQ 

since  in  the  above  measurements  P  has  been  made  equal  to  unity. 
Hence  in  general  the  potential-difference  which  exists  between  an 
electrode  and  a  solution  of  an  ion  concentration  P,  at  a  temperature 
T,  is  as  follows:  — 

1  Approximately. 

2  The  sign  becomes  +  when  negative  ions  are  formed. 


ELECTROMOTIVE  FORCE  249 

"DfT\ 

^electrode-  electrolyte  =  (EP)  +  ~  ln  P1 


when  the  electrode  sends  positive  ions,  and 


VQ 

when  it  sends  negative  ions,  into  the  solution. 

The  electrolytic  potentials  for  solvents  other  than  water  cannot 
yet  be  given,  since  the  degrees  of  dissociation  involved  are  not  known. 
The  potential-differences  of  a  large  number  of  couples  with  organic 
solvents  have  been  measured  by  Kahlenberg.1 

Finally,  attention  is  called  to  the  fact  that  the  HelmHoltz  equation, 


is  applicable,  not  only  to  the  electromotive  force  of  the  entire  cell, 
but  also  to  the  constituent  potential-differences  of  each  individual 
reversible  electrode.  This  has  been  shown  to  be  true  experimentally 
by  Jahn2  for  several  metal  electrodes.  In  this  equation  Q  represents 

dF 
the  heat  effect  of  the  reaction  at  the  electrode  in  question,  and  — 

the  temperature  coefficient  of  the  potential-difference  in  question. 
Just  as  the  total  electromotive  force  of  the  cell  is  made  up  of  two  or 
more  independent  potential-differences,  so  the  temperature  coefficient 
of  the  former  is  made  up  of  the  sum  of  the  individual  temperature 
coefficients  of  the  latter. 

The  expression,  - 


represents  what  is  known  as  the  Helmholtz  —  or  Peltier  —  heat 
effect.  It  was  first  applied  to  simple  metallic  contacts.  In  the 
case  of  such  contacts,  the  Peltier  effect  is  understood  to  mean  the 
quantity  of  heat  which  is  evolved  or  absorbed  when,  at  the  tempera- 
ture of  the  contact,  a  unit  quantity  of  electricity  passes  through  the 
contact.  The  Peltier  effect  is  the  reverse  of  the  thermoelectric  phe- 
nomenon discovered  by  Seebeck  which  was  mentioned  on  page  228. 
Influence  of  Negative  Ions  upon  the  Potential-difference  :  Metal  — 
Metal  Salt  Solution.  —  The  question  may  still  be  asked:  Is  the 
nature  of  the  negative  ion  without  influence  upon  the  potential-dif- 
ference ?  To  answer  this  question,  Neumann  prepared  0.01  nor* 

1  J.  Phys.  Chem.,  3,  379  (1899). 

*  Ztschr.  phys.  Chem.,  18,  399  (1896).       . 


250  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

mal  solutions  of  over  twenty  different  thallium  salts  (mostly  of 
organic  acids),  and  determined  the  potential-differences  between 
them  and  pure  metallic  thallium.  In  these  solutions,  these  salts 
may  be  considered  to  be  equally  dissociated,  and  the  same  potential- 
differences  might  be  expected  in  each  case.  As  the  measured  values 
do  not  differ  by  more  than  0.001  of  a  volt,  it  is  a  justifiable  conclu- 
sion that  the  nature  of  the  negative  ion  is  without  influence  upon  the 
potential-difference  between  metal  and  solution. 

Nevertheless  nitrate  solutions  differ  considerably  from  chloride 
solutions.  These  apparent  exceptions  to  the  above-stated  general- 
ization may  be  explained  by  the  fact  that  in  the  latter  case  the  con- 
centration of  the  thallo  ions,  which  determine  the  potential-difference, 
is  less  than  in  the  former  case,  due  to  the  formation  of  complexes. 
On  the  whole,  such  an  indirect  influence  of  the  anion  is  not  seldom 
in  the  case  of  metal  salt  solutions.  The  degree  of  complex  forma- 
tion depends  on  the  electro-affinity  of  the  anion.1 


CELLS  IN  WHICH   THE   ELECTROMOTIVELY  ACTIVE 
SUBSTANCES  ARE  NOT  ELEMENTS 

A  class  of  chemical  cells,  apparently  very  different  from  that  rep- 
resented by  the  Daniell  element,  will  now  be  considered.  If  a  plat- 
inized platinum  electrode  is  surrounded  by  a  solution  of  stannous 
chloride,  and  another  by  one  of  ferric  chloride,  and  the  two  are 
placed  in  metallic  connection,  an  electric  current  is  obtained,  which 
passes  through  the  cell  from  the  former  solution  to  the  latter.  The 
trivalent  ferric  ions  give  up  an  equivalent  of  electricity,  becoming 
ferrous  ions,  while  each  stannous  ion  takes  up  two  electrical  equiva- 
lents, becoming  a  stannic  ion,  as  follows  :  — 

Sn"  -f-  2  Fe"'  =  Sn""  -f  2  Fe". 

The  process  may  be  imagined  in  detail  as  follows  :  The  stannous 
ions  change  into  stannic,  and  thereby  positive  electricity  is  con- 
sumed. This  is  shown  by  the  equation, 


Since  this  can  never  take  place  alone  in  a  change  of  chemical  into 
electrical  energy,  the  same  quantity  of  negative  electricity  must 
be  produced  upon  the  electrode.  This  electricity  passes  through 
the  wire  to  the  other  electrode,  where  it  unites  with  the  positive 

1  Abegg-Labendzinski,  Ztschr.  Elektrochem.,  10,  77  (1904). 


ELECTROMOTIVE   FORCE  251 

electricity  derived  from  the  change  of  ferric  into  ferrous  ions,  ac- 
cording to  the  equation, 

2Fe"*-t-2Q(-)=2Fe". 
The  cell 

Hydrogen  (in  platinum)  —  electrolyte  -4—, 
Chlorine  (in  platinum)  —  electrolyte  B ! 

is  evidently  completely  analogous  to  the  above  combination.  It 
was  previously  stated  (page  194)  that  platinized  platinum  in  hydro- 
gen may  be  considered  as  a  hydrogen  electrode.  In  a  similar  man- 
ner the  above  combination  may  be  characterized  as  stannous  and 
ferric  electrodes,  and  just  as  a  tendency  to  go  into  the  ionic  (or  of 
the  ions  to  go  into  the  neutral)  state  was  ascribed  to  the  hydrogen 
and  chlorine  electrodes,  so  a  tendency  of  the  stanuous  and  ferric  to 
form  stannic  and  ferrous  ions  may  be  recognized.  The  electromo- 
tive force  of  this  cell  also  consists  principally  of  the  two  indepen- 
dent potential-differences  occurring  at  the  electrodes.  But  these 
potential-differences  depend  not  only  upon  the  transformatian  pres- 
sures (which  are  analogous  to  the  solution  pressure)  of  the  sub- 
stances in  question,  but  also  upon  the  osmotic  pressures  of  the  ions 
forming.  Therefore  the  concentrations  of  the  stannic  ions  formed 
at  the  one  electrode,  and  of  the  ferrous  ions  at  the  other,  are 
important  factors;  a  certain  constant  potential-difference,  as  in 
the  Daniell  cell,  could  only  be  expected  when  the  solutions 
already  contained  stannic  and  ferrous  ions.  Moreover,  the  con- 
centration of  the  altering  compounds  must  be  considered,  for  the 
transformation  pressure  of  a  substance  at  constant  temperature  is 
invariable  only  at  a  definite  concentration. 

From  what  has  been  said,  it  is  obvious  that  there  is  essentially  no 
difference  between  the  Daniell  and  the  so-called  reduction  and  oxidation 
cells.  The  laws  governing  the  former  may  be  expected  to  control  the 
latter. 

Already  in  the  first  edition  of  this  book  (1895)  this  same  ex- 
planation was  given.  At  that  time,  however,  a  proof  of  them  was 
not  possible  because  of  lack  of  experimental  results.  Thus  the  in- 
fluence of  the  concentration  of  the  substances  formed  at  the  elec- 
trodes has  been  almost  entirely  neglected,  and  it  is  probable  that 
the  varying  values  of  such  cells  are  due  to  this.  The  non-reversi- 
bility of  these  cells  may  be  similarly  accounted  for.  If,  instead  of 
allowing  the  stannous  chloride  —  ferric  chloride  cell  to  act,  it  be 
opposed  by  a  cell  of  greater  electromotive  force,  oxygen  must  sepa- 
rate at  one  electrode  (at  least  in  dilute  solution)  and  metallic  tin  at 


252  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

the  other.  Stannic  and  ferrous  chlorides  being  present,  a  change 
of  the  stannic  into  the  stannous,  and  of  ferrous  into  ferric  salt, 
when  the  current  is  not  too  strong,  would  certainly  take  place  in- 
stead of  the  above,  and  the  cell  be  reversible. 

A  cell  which  consists  of  zinc  and  chlorine  electrodes,  and  of  electro- 
lytes which  do  not  contain  zinc  and  chlorine  ions,  is  also  not  a  reversi- 
ble cell.  If  a  stronger  opposing  current  be  sent  through  such  a  cell, 
the  positive  ions  of  one  electrolyte  separate  at  the  zinc,  and  the 
negative  of  the  other  at  the  chlorine  electrode,  while  zinc  and  chlo- 
rine ions  are  liberated  through  its  own  activity  as  a  cell. 

Equations  may  be  deduced  for  the  calculation  of  the  electromo- 
tive force  of  such  cells.  They  are  analogous  to  those  formulated 
for  the  Daniell  cell.1 

Every  process  which  takes  place  at  an  electrode  of  a  cell  during 
its  activity  may  be  represented  by  the  following  scheme  :  — 

aA  +  bB  ----  f-VQ  (+)^:dD  +  eE  •». 

Here  a  b,  •••  represent  the  number  of  mols  of  the  substances  A, 
B,  •••  which  by  taking  on  the  quantity  of  positive  or  giving  off 
the  quantity  of  negative  electricity,  VQ,2  form  d,  e,  •••  mols  of  the 
substances  Z),  JS,  •••.  By  an  application  of  this  scheme  to  the 
ferri-ferro  electrode,  the  following  equation  is  obtained  :  — 


The  left-hand  side  of  this  equation  represents  the  higher  state  of 
reduction  or  the  lower  state  of  oxidation.  The  upper  arrow  of  the 
transformation  sign,  then,  represents  an  oxidation,  while  the  lower 
one  represents  a  reduction. 

As  already  indicated,  the  assumption  that  the  potential-difference 
at  the  electrode,  not  only  in  the  case  of  the  Daniell  cell  but  in  gen- 
eral, is  dependent  on  the  concentration  of  the  substance  being  formed 
as  well  as  on  that  of  the  substance  being  consumed,  in  the  manner 
required  by  the  Nernst  logarithmic  equation,  seems  plausible.  If  all 
the  substances  under  consideration  be  taken  at  unit  concentration, 
i.e.  usually  one  mol  (or  one  ion-mol)  per  liter,  and  if  the  value  in 
this  case  of  the  potential-difference, 

^electrode  —  electrolyte? 

1  See  also  Ostwald-Luther,  Physiko-chemische  Messungen,  p.  373  ;  Ztschr. 
Elektrochem.,  7,  1043  (1901). 

2  In  passing  from  metallic  to  ionic  state,  v  =  valence  of  the  ion  formed.     See 
also  page  182. 


ELECTROMOTIVE  FORCE  253 

be  represented  by  FO,  then,  accepting  the  correctness  of  the  above 
assumption,  the  following  equation  is  obtained  for  the  potential- 
difference  at  an  electrode  when  the  electrolyte  is  of  any  concentra- 
tion C:  — 

RT       CB*CB- 


The  higher  state  of  oxidation  is  represented  in  the  numerator  and 
the  lower  state  in  the  denominator.  The  former,  then,  becomes  trans- 
formed into  the  latter  by  giving  up  positive  or  taking  on  negative 
electricity.  In  regard  to  the  sign  of  F  or  FO,  the  rule  given  on  page 
244  is  to  be  followed.  The  value  of  FO  may  also  appropriately  be  con- 
sidered as  the  electrolytic  potential  (EP).  For  the  ferri-ferro  elec- 
trode, the  following  equation  should  hold  :  — 

^electrode-  electrolyte  =  Fo  +  RTllL  ~^rt 

where  Fe'"  and  Fe"  represent  the  concentrations  or  the  osmotic 
pressures  of  the  ferro  and  ferri  ions  respectively.  This  expression  is 
entirely  analogous  to  that  which  holds  for  metal  electrodes.  Applied 
to  the  hydrogen  and  chlorine  electrodes,  the  equation  assumes  the 
following  forms  :  — 

RT,    in. 

lelectrode  -  electrolyte  ==  ¥.0  +    ^  Q          H 


»A*« 

£  electrode  -  electrolyte  ~  £  0      '      O  Q     r\\  /2 

For  an  oxygen  electrode,  two  different  expressions  hold  according 
as  the  equation, 

02  +  4q  (_),=  20'V 
or  the  equation, 

O2  +  2  H20  +  4g  (-)  3:  4  OH', 

be  considered  to  take  place.1    The  equation  which  holds  in  the 

former  case  is  as  follows  :  — 

RT         O2 

?"electrode-  electrolyte—  So  '  "H     ~~    1 


1  The  following  relation  exists  :  — 

2  OH'  ^  H2O  +  O". 

The  concentration  of  the  OH  ions,  but  not  that  of  the  O  ions,  can  be  obtained 
experimentally.  The  latter  is  certainly  very  small.  In  a  consideration  of  equi- 
librium states  it  makes  no  difference  whether  OH'  or  O"  ions  are  involved. 


254  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

Here  FO"  represents  the  (EP),  or,  in  words,  the  potential-difference 
which  exists  when  the  oxygen  is  under  a  pressure  of  one  atmosphere 
and  is  in  contact  with  a  solution  which  contains  one  gram-ion  of 
oxygen  ions  per  liter.  The  equation  which  holds  in  the  second 
case  is 

C\ 


?   electrode  -  electrolyte  ~  Si  Y  ~        A  Q  /(")  TT'\4 

The  value  of  FO'"  is  determined  by  the  fact  that  the  oxygen  is  under 
a  pressure  of  one  atmosphere  and  is  in  contact  with  a  normal  solu- 
tion of  hydroxyl  ions.  Strictly  speaking,  the  value  H20  should 
appear  in  the  numerator  of  the  fraction  the  logarithm  of  which  is  to 
be  taken.  Since,  however,  the  concentration  of  the  water  is  not  appre- 
ciably changed  during  the  reaction,  its  mass-action  effect  can  be  left 
out  of  consideration.  In  fixing  the  value  of  FO'",  the  concentration 
of  the  water  in  the  solution  may  be  placed  equal  to  unity.  It  very 
often  happens  that  water  takes  part  in  a  reaction  in  this  manner. 
Assuming  that  the  following  reaction  takes  place  at  a  permanganate 
electrode, 

MnO'4  +  8  H'  +  5g  (-)  ;£  Mn"  +  4  H20, 

then  the  strict  equation  would  be 

RT       MnO'4  x  H' 

FWrode-electrolyte  -  ?0  +     ^    ln  Mn"  X  (H20)4  ' 

As  in  the  case  of  the  metals,  so  in  the  case  of  other  oxidizing  or 
reducing  substances,  the  determination  of  (EP)  is  of  importance. 
Very  little  in  this  direction  has,  however,  been  done.  Below  a 
few  accurate  values  are  given  :  — 

ELECTRODE  ^ELECTRODE  •<—  ELECTROLYTE 

Ferri-ferro  +0.46    volt 

Cupri-cupro  +  0.13    volt 

Ferri-ferrocyanide  H-  0.153  volt 

Thalli-thallo  +  0.908  volt 

Measurements  have  been  made  to  confirm  the  statement  that  the 
electromotive  force  varies  with  the  concentration  of  the  substances 
involved  as  required  by  the  above  equation  by  Peters,1  Schaum,2  Fre- 

1  Ztschr.  phys.  Chem.,  26,  193  (1898). 

2  Sitzber.  d.  G.  zur  Beforderung  d.  Naturw.,  Marburg,  No.  7,  1898. 


ELECTROMOTIVE  FORCE  255 

denhagen,1  Spencer-Abegg,2  Maitland-Abegg,3  and  Sammet-Luther.4 
Their  results  are  in  good  agreement  with  the  theory. 

The  results  given  in  the  last-named  investigation  will  be  consid- 
ered again  in  the  discussion  of  equilibrium  constants.  Other  (EP) 
values  will  then  be  given.  At  this  point  attention  will  be  called 
only  to  the  possibility  of  determining  the  electromotive  valence,  i.e. 
the  number  of  chemical  equivalents  of  electricity  Q  required  for 
the  electrolytic  oxidation  or  reduction  of  the  reacting  substances, 
from  the  dependence  of  the  electromotive  force  on  the  concentration. 
If  the  process  takes  place  in  stages,  as  in  the  case  of  the  reduction 
of  molybdic  acid  solutions  through  intermediate  pentavalent  to 
trivalent  molybdinum,  it  may  be  perceived  by  means  of  continued 
potential  measurements,  the  influence  of  the  concentrations  of  the 
individual  reacting  substances  being  taken  into  consideration.  An 
insight  into  the  mechanism  of  electrolytic  processes  may  thus  be 
obtained.5 

It  scarcely  needs  to  be  mentioned  that,  when  two  single  potential- 
differences  are  combined  to  form  a  cell,  the  electromotive  force  of 
the  cell  is  essentially  equal  to  their  sum.  This  was  proven  by  Ban- 
croft.6 Although  his  results  suffered  from  the  lack,  at  that  time,  of 
known  ion  concentrations,  the  values  of  the  single  potential-differ- 
ences measured  are  given  here  because  they  are  of  considerable 
interest  and  because  they  are  a  measure  of  the  strength  of  the  oxi- 
dizing or  reducing  power  of  the  substances.  They  were  obtained 
with  the  use  of  platinized  electrodes  surrounded  by  the  liquids  men- 
tioned. Most  of  the  solutions  contain  about  \  mol  per  liter. 

It  is  evident  from  the  preceding  discussion  that  in  electrical  pro- 
cesses it  is  possible  to  distinguish  sharply  between  oxidations  and 
reductions.  In  the  case  of  such  processes,  a  substance  is  said  to  be  oxi- 
dized when  its  positive  charge  of  electricity  is  increased  or  its  negative 
charge  decreased.  It  is  said  to  be  reduced  when,  conversely,  its  nega- 
tive charge  is  increased  or  its  positive  charge  is  decreased. 

An  actual  oxidation,  i.e.  interaction  with  oxygen,  although  for- 
merly always  believed  to  take  place,  is  in  many  cases  not  involved. 
The  action  consists,  instead,  of  a  change  of  the  charges  on  the  ions. 
The  term  oxidation  is,  however,  still  retained. 

*  Ztschr.  anorg.  Chem.,  29,  396  (1902). 

*  Ztschr.  anorg.  Chem.,  44,  379  (1905). 
^  Ztschr.  Elektrochem.,  12,  263  (1906). 

*  Ztschr.  Elektrochem.,  11,  293  (1905);  Ztschr.  phys.  Chem.,  53,  641  (1905). 
»Chilesotti,  Ztschr.  Elektrochem.,  12,  173  (1906). 

«  Ztschr.  phys.  Chem.,  10,  387  (1892),  and  14,  228  (1894X 


256 


A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 


SOLUTIONS  OF 

51C  electrode  —  electrolyte 

SOLUTIONS  OF 

2EC  electrode  —  electrolyte 

Sn  C12  4  KOH  .     . 
Na2S    . 

-  0.861 
—  0  651 

FeS04,  neutral 
Hydroxylamine 

4-  0.073 
4-  0076 

Hydroxylamine, 
KOH     .... 
Chromous  acetate, 
KOH    .... 

Pyrogallol,  KOH   . 
Hydrochinone 

-  0.616 

-  0.589 
-  0.482 
—  0  329 

NaHS03   .... 
H2S03      .... 
FeS044H2S04  .     . 
Potassium      ferric 
oxalate      .     .     . 
I2,  KI  .     .     .     . 

+  0.103 
4-  0.158 
+  0.234 

4  0.286 
4-  0  328 

Hydrogen,  HC1      . 
Potassium    ferrous 
oxalate 

-  0.311 
—  0275 

K3Fe(CN)6  .  .  . 
K2Cr2O7  .... 
KNO3  

4  0.422 
+  0.502 
4  0.577 

Chromous  acetate 
K4Fe(CN)6    KOH 

-0.196 
—  0  086 

C12,  KOH  .  .  . 

FeCl3 

4  0.626 
+  0  678 

I2,  KOH  .... 

-  0.070 

HNO3  

4-  0.697 

Sn  C12,  HC1  .     .     . 
Potassium      arsen- 
ate  

,     -  0.064 
-0054 

HC1O4  .... 
Br2,  KOH  .  .  . 
H2CrfO7  . 

+  0.707 
4-  0.755 
4  0.837 

NaH2POa      .     .     . 
CuCl2  

-  0.044 
4-  0.000 

HC103  .... 
Br2,  KBr  .  .  . 

4  0.856 
4  0.865 

Na2S203   .     .     . 

+  0016 

KIO3  

4-  0.929 

Na2S03     .... 
Na2HPO3      .     .     . 

K4Fe(CN)6  .     .     . 

+  0.023 
+  0.033 
4-  0.035 

Mn02,KCl  .  .  . 
C12,  KC1  .... 
KMnO4  .... 

4-  1.068 
41.106 
4  1.203 

According  to  these  definitions  there  must  be,  in  every  galvanic 
cell,  an  oxidation  at  one  electrode  and  a  reduction  at  the  other. 
In  the  Daniell  cell  the  reduction  takes  place  at  the  zinc  electrode 
and  the  oxidation  at  the  copper.  The  precipitation  of  one  metal  by 
another,  the  process  of  substitution,  is  thus  to  be  considered  as  one 
of  oxidation  and  reduction.  It  is  evident,  then,  that  the  metals  can 
only  serve  as  reducing  agents,  since  they  are  only  capable  of  produc- 
ing positive  ions,  followed  by  the  formation  of  negative  or  the  dis- 
appearance of  positive  ions.  The  metals  themselves  are  thereby 
oxidized. 

On  the  other  hand,  all  of  those  elements  which  produce  negative 
ions  act  exclusively  as  oxidizing  agents.  Solutions  of  electrolytes 
in  general  may  be  reducing  as  well  as  oxidizing  agents,  for  they  con- 
tain both  positive  and  negative  ions,  and  are  therefore  capable  of 
yielding  positive  or  negative  electricity.  If  zinc  be  placed  in  a  so- 
lution of  cadmium  bromide,  cadmium  is  precipitated,  the  solution 
acting  as  an  oxidizing  agent ;  but  if  chlorine  be  conducted  into  the 
solution,  bromine  separates,  the  solution  acting  as  reducing  agent. 


ELECTROMOTIVE   FORCE  257 

Similarly,  the  substances  in  the  above  table  may  be  examined  to 
discover  whether  they  are  reducing  or  oxidizing  agents.  From  the 
above  it  is,  moreover,  not  surprising  that  a  dissolved  substance  may 
have  a  reducing  or  oxidizing  action  according  to  circumstances. 
This  may  even  be  the  case  when  only  the  single  ion  enters  the  reac- 
tion ;  the  bivalent  ferrous  ion  may  change  into  the  trivalent  ion,  on 
the  one  hand,  or  into  metallic  iron,  on  the  other  ;  that  is,  it  may  act 
reducing  or  oxidizing. 

Attention  has  been  called  by  Luther1  to  the  fact  that  since  the 
change  in  free  energy  in  an  isothermal,  reversible  process  is  inde- 
pendent of  the  path  and  dependent  only  on  the  original  and  final 
states,  the  work  required  to  transform  the  lower  directly  into  the 
highest  state  of  oxidation  is  equal  to  the  work  required  to  effect  the 
transformation  from  the  lower  to  the  next  higher  state  plus  the 
work  required  to  transform  the  latter  to  the  highest  state  of  oxida- 
tion, etc.  Since,  now,  the  work  for  the  reversible  oxidation  is  meas- 
ured by  the  quantity  of  electricity  consumed,  the  following  holds  :  — 


(a  +  b)  QF  =  aoX  +  &QF". 

Here  a  and  b  represent  the  numbers  of  electrical  units  Q  of  elec- 
tricity consumed  in  changing  the  state  of  oxidation  from  the  lower 
to  the  intermediate,  and  from  the  intermediate  to  the  higher  state, 
respectively.  The  electromotive  force  required  during  the  first 
stage  of  the  oxidation  is  F',  and  during  the  second  stage  F",  while 
that  required  when  the  entire  oxidation  takes  place  in  one  stage  is 
F.  From  the  above  equation  the  following  is  obtained  :  — 


a  +  b 

In  the  case  of  iron,  which  may  furnish  either  di-  or  trivalent  ions, 
this  equation  becomes 

_2Ff  +  F" 

~3       ' 

and  in  the  case  of  copper,  which  may  furnish  uni-  and  bivalent  ions, 
it  becomes 

r-*'+F" 

2 

These  equations  state  that  the  electromotive  force  which  is  re- 

1  Ztschr.phys.  Chem.,  34,  488  (1900),  and  36,  385  (1901).  The  numerical 
values  have  been  changed  to  agree  with  more  recent  measurements.  See  previ- 
ous pages. 


258  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

quired  to  carry  out  the  oxidation  in  one  stage  from  the  lowest  to  the 
highest  state,  is  always  between  the  two  electromotive  forces  which 
are  required  to  carry  out  the  oxidation  from  the  lowest  to  the  inter- 
mediate, and  from  the  intermediate  to  the  highest  state,  respect- 
ively. Hence,  such  a  relation  as, 


", 


which  at  first  sight  one  might  hit  upon,  does  not  hold. 

Nothing  can  be  predicted  in  regard  to  the  order  of  the  three  elec- 
tromotive forces,  since  they  depend  both  upon  the  nature  of  the 
substances  and  upon  the  concentrations  involved.  If  the  latter  con- 
dition be  eliminated  by  taking  all  substances  involved  at  a  concen- 
tration unity,  then  two  typical  cases  may  occur. 

CASE  I.  Iron  is  an  example  of  this  case.  When  two  of  the  values 
are  known,  evidently  the  third  one  may  be  calculated.  Thus  for 
iron 

z'  =  2C  re  —  >.  re-  =  —  0.  94  volt,  and 

F"  =  FC  Electrodes-Electrolyte^  =  +  °'46  Vo1^ 

has  been  found.     It  follows,  then, 

E  =  Ic  Fe—  >.  Fe"-  =  ~  0-^7  Volt. 

The  order  is,  therefore,         F',  F,  and  F", 

or,  in  other  words,  the  strongest  reducing  process  is  that  correspond- 
ing to  F'  and  the  strongest  oxidizing  process  is  that  corresponding 
to  F". 

Leaving  out  of  consideration  the  negative  ions,  in  the  cell, 

Iron—  ferrous  ions  --------------------  -  ,^ 

Platinum  —  ferrous  and  ferric  ions  -----  •' 


the  iron  electrode  is  negative,  and  the  platinum  electrode  positive. 
When  the  cell  is  active,  the  quantity  of  iron  and  ferric  ions  de- 
creases, while  that  of  the  ferrous  ions  increases.  In  the  cell,  there- 
fore, the  same  action  takes  place  as  would  take  place  if  the 
substances  at  the  same  concentration  were  directly  mixed,  i.e.  for- 
mation of  the  intermediate  state  of  oxidation  at  the  expense  of  the 
other  two,  according  to  the  equation, 


Besides  the  above  cell  (1),  two  more  may  be  formed  by  combin- 
ing the  three  potential-differences.     They  are  as  follows  :  — 


ELECTROMOTIVE   FORCE 


259 


and 


Iron  —  ferrous  ions ; 

Iron  —  ferric  ions '' 


Iron  —  ferric  ions 

Platinum  —  ferrous  and  ferric  ions 


(2) 
(3) 


In  these  cells  also,  when  a  current  flows,  the  intermediate  stage, 
of  oxidation  is  formed  at  the  expense  of  the  other  two. 

There  are  interesting  relations  which  exist  between  these  three 
cells.  If  the  electromotive  forces  of  the  cells  be  calculated  from 
the  single  potential-differences,  the  following  values  are  obtained :  — 


CELL 


ELECTROMOTIVE  FORCE 


(1) 
(2) 
(3) 


1.40  volts 
0.47  volt 
0.93  volt 


If,  further,  the  number  of  units  of  electricity  Q  which  must  be 
passed  through  each  cell  in  order  to  dissolve  56  grains  of  metallic 
iron  be  calculated,  the  values  obtained  are  as  follows :  — 


CELL 


COULOMBS 


(1) 
(2) 
(3) 


2Q 
6Q 
3Q 


Hence  the  quantity  of  energy  obtainable  from  the  process, 
2  Fe"*  +  Fe  =  3  Fe", 

may  be  obtained  in  any  one  of  the  following  three  forms  according 
to  the  cell  used :  — 


CELL 


FORM 


(1) 
(2) 


1.40  volts  x  2Q 
0.47  volt  x  6  Q 
0.93  volt  x  3  Q 


Naturally,  the  product  is  in  all  cases  equal  to  2.80  x  96,540  joules. 
It  is  evident  that  here  a  true  galvanic  transformation  of  energy  is 
being  dealt  with,  which  is  thereby  characterized  that  only  such 


260  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

transformation  relations  can  appear  as  can  be  expressed  in  whole 
numbers.  Whether  or  not  all  these  cells  can  be  realized  is  another 
question. 

CASE  II.  Copper  is  an  example  of  this  case.  The  action  is  here 
the  opposite  of  that  in  the  case  of  iron,  i.e.  the  lower  and  higher 
states  of  oxidation  increase  spontaneously  at  the  expense  of  the 
intermediate  state,  as  follows :  — 

2  Cu*  =  Cu  +  Cu". 
When  the  cell, 


Copper  —  cuprous  ions 

Platinum  —  cuprous  and  cupric  ions- 


(which,  however,  cannot  be  directly  realized  because  of  the  unstable 
character  of  the  cuprous  ions),  is  in  action  cuprous  ions  must  disappear 
and  cupric  ions  appear.  In  other  words,  the  platiDum  pole  must  be 
negative  and  the,  copper  pole  positive.  Corresponding  to  this,  the 
order  of  the  electromotive  forces  is  the  reverse  of  that  in  the  case  of 
the  iron,  being 

F",  F,  and  F'. 

In  this  case,  the  process  corresponding  to  F"  is  most  strongly 
reducing,  while  that  corresponding  to  F'  is  most  strongly  oxidizing. 

It  is  characteristic  of  all  such  cases  as  that  of  copper  that  on  the 
one  hand  the  intermediate  stage  Cu*  is  more  strongly  oxidizing 
than  the  highest  stage  Cu",  and  on  the  other,  it  produces  a  stronger 
reducing  influence  than  does  the  lowest  stage  Cu.  Furthermore, 
other  conditions  remaining  the  same,  the  activity  of  the  intermediate 
stage  both  as  an  oxidizing  and  as  a  reducing  agent  increases  with 
increasing  concentration. 

Although  it  sounds  paradoxical,  by  the  oxidation  of  metallic 
copper  a  stronger  reducing  agent  Cu',  and  by  the  reduction  of 
cupric  ions  a  stronger  oxidizing  agent  Cu',  is  obtained.  In  other 
words,  it  may  be  stated  that,  by  the  addition  of  a  positive  charge, 
the  oxidizing  power,  and  by  the  removal  of  a  positive  charge,  the 
reducing  power,  of  a  substance  may  be  increased. 

Considering,  finally,  an  iron  electrode  (the  same  holds  for  a  cop- 
per electrode)  in  contact  with  a  solution  with  ferrous  and  ferric 
ions  in  such  concentrations  that 


and  equilibrium  exists  at  the  electrode.     The  relation 


ELECTROMOTIVE   FORCE  261 

is  then  obtained  directly  from  Luther's  equation.  Hence  when 
equilibrium  is  established,  the  three  potential-differences  are  always 
equal  to  each  other. 

It  may  be  well  to  say  a  word  here  concerning  the  conditions  which 
determine  the  actual  production  of  the  electric  current.1  It  has  been 
seen  that  in  all  galvanic  cells  a  reduction  and  oxidation  take  place ; 
that  is,  at  one  electrode  ions  come  into  existence,  and  at  the  other 
ions  disappear.  TJiat  the  reaction  may  be  the  source  of  an  electric 
current,  the  two  processes  must  take  place  at  points  separated  from 
each  other.  If  they  both  occur  at  the  same  point,  no  electric 
current  can  be  obtained.  Zinc  being  placed  in  a  copper  sulfate 
solution,  both  the  oxidation  and  reduction  proceed  simultaneously 
at  the  surface  of  the  metal.  The  electric  charges  of  the  dissolving 
zinc  and  precipitating  copper  have  the  opportunity  of  neutralizing 
each  other  there,  and  the  possibility  of  a  removal  of  this  neutraliza- 
tion to  some  other  point  (and  thereby  the  production  of  an  electric 
current)  is  lost.  Hence  the  general  statement,  that  a  chemical  reaction 
between  two  substances  can  only  be  used  as  a  source  of  electrical 
energy  when  electricity  is  produced  or  disappears  during  the  reaction 
(i.e.  by  changes  in  the  charges  of  the  ions),  and  also  when  the  two  sub- 
stances separated  from  each  other  are  still  capable  of  undergoing  this 
reaction. 

If  zinc  be  in  contact  with  a  solution  of  zinc  sulfate,  and  a 
platinum  wire  be  placed  therein,  only  a  feeble  current  is  obtained 
on  connecting  the  wire  with  the  zinc.  If  it  be  desired  to  dissolve 
the  zinc  rapidly,  that  is,  to  cause  it  to  pass  into  the  ionic  state  and 
produce  a  large  current,  this  may  be  accomplished  by  surrounding  the 
platinum  with  a  solution  such  as  that  of  a  copper  salt,  or  of  an  acid 
whose  positive  component  has  a  smaller  tendency  to  produce  ions 
than  zinc.  The  addition  of  the  copper  or  acid  solution  directly  to 
the  zinc  solution  would  evidently  not  produce  an  electric  current. 

In  the  production  of  galvanic  currents  many  different  oxidizing 
agents  have  been  used  to  achieve  the  highest  possible  efficiency, 
without  the  theory  of  the  phenomena  being  clearly  understood.  One 
of  the  most  common  cells  is  the  bichromate  cell,  consisting  of 

Zn  -  H2Cr AC^Cr  A  +  H2S04)  -  C. 

The  process  consists  essentially  in  the  formation  of  zinc  ions  at  the 
negative  (zinc)  electrode,  and  the  reduction  of  chromium  ions  at  the 
positive  (carbon)  electrode  from  higher  to  lower  valency,  whereby 
electricity  is  given  up  to  the  electrode. 

1  Ostwald,  "  Chemische  Ferae wirkung,"  Ztschr.  phys.  Chem.,  9,  540  (1892). 


262  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

The  electromotive  force  of  this  cell  is  great,  because  the  zinc  has 
a  strong  tendency  to  go  into  the  ionic  state,  and  the  chromium  ions  of 
high  valency  also  tend  strongly  to  change  into  ions  of  lower  valency, 
the  two  tendencies  additively  producing  the  high  electromotive  force. 
Furthermore,  it  is  clear  that  the  electromotive  force  of  this  cell, 
when  active,  must  gradually  diminish,  because  zinc  ions  are  con- 
tinually forming,  while  the  concentration  of  the  chromium  ions  of 
higher  valency  is  decreasing,  and  that  of  those  of  lower  valency  in- 
creasing. Each  of  the  three  changes  reduces  the  electromotive  force. 

The  energetic  oxidation  of  the  zinc  and  the  high  electromotive 
force  of  the  cell  is  therefore  obtained  by  the  addition  of  the  oxidiz- 
ing agent,  not  to  the  zinc,  but  to  the  carbon. 

It  is  also  possible  to  dissolve  the  noble  metals  or  to  change  them 
into  the  ionic  state  in  a  similar  manner.  A  cell  consisting  of 

Pt  —  NaCl  solution  —  Au 

produces  no  electric  current,  though  one  is  produced  when  chlorine 
water  is  introduced  at  the  platinum  electrode,  the  gold  dissolving. 
The  great  tendency  of  the  chlorine  to  yield  ions  may  be  looked  upon 
as  forcing  the  resisting  gold  to  act  similarly.  Addition  of  the 
chlorine  water  to  the  gold  electrode  alone  would  not  result  in  the 
production  of  a  current  (the  platinum  being  unaffected),  and  the  gold 
would  oxidize  very  slowly. 

The  free  energy  of  other  processes,  such  as  that  of  solution,  can  be 
made  to  produce  an  electromotive  force  by  being  coupled  or  combined 
with  oxidation  or  reduction  processes.1  Thus  the  double  cell, 

H2(in  Pt)  —  saturated  solution  over  solid  salt  —  02(in  Pt) 

H2(in  Pt)  —  pure  water 02(in  Pt) !> 

produces  an  electric  current  which  flows  from  the  saturated  solution 
through  the  oxygen  electrode  to  the  pure  water.  The  process  which 
takes  place  when  the  cell  is  in  action  is  merely  the  combining  of 
water  with  solid  salt  to  form  a  saturated  solution.  Since  this  pro- 
cess can  in  this  manner  be  carried  out  reversibly,  the  electrical 
energy  derivable  from  it  gives  directly  the  maximum  available  work 
of  the  process.  As  a  matter  of  fact,  the  same  relations  have  been 
considered,  only  from  a  different  standpoint,  earlier  in  the  book, 
especially  in  the  section  on  double  concentration  cells  (see  page  211). 
Finally,  the  above  cell  shows  clearly  that  the  active  mass  of  the 
Yvrater  in  the  solution  is  not,  as  has  been  tacitly  assumed  up  to  this 

1  Ostwald-Luther,  Hand-  und  Hilfsbuch,  p.  388. 


ELECTROMOTIVE  FORCE  263 

point,  equal  to  that  of  pure  water.     It  is  proportional  to  the  vapor 
pressure.     In  the  case  of  dilute  solutions,  however,  the  difference 
between  the  active  masses  of  pure  water  and  solution,  and  therefore 
also  the  electromotive  force  of  the  cell,  is  very  small.     Since  the 
active  mass  varies,  the  product  H'  x  OH'  must  also  change;  for  if  it 
remaiDed  constant,  then,  considering  the  above  cell  as  a  combina- 
tion of 

Hydrogen  -----------  H'  _______ 

and  Oxygen  --------------  OH'  ______ 

electrodes,  no  electromotive  force  could  arise. 

FORMATION  OF  POTENTIAL-DIFFERENCE  AT  THE  ELEC- 
TRODES. SPONTANEOUS  EVOLUTION  OF  OXYGEN  OR 
HYDROGEN.  THE  PROCESS  OF  CURRENT  PRODUCTION1 

In  considering  any  electrode  and  an  aqueous  solution  of  the  cor- 
responding ions,  between  which  there  exists  an  electromotive  force 
F,  it  must  not  be  forgotten  that  there  are  also  hydrogen  and  hydroxyl 
(or  oxygen)  ions  present  in  the  water.  Hence  in  order  that  equilib- 
rium may  be  established,  each  electrode  must  become  charged  with 
hydrogen  and  oxygen  to  such  an  extent  that  the  potential-difference 
of  the  combination,  — 

Hydrogen  —  hydrogen  ions  —  , 
and  of  the  combination,  — 

Oxygen  —  oxygen  ions  —  , 

is  equal  to  F.  In  this  connection,  the  reader  is  referred  to  the  dis- 
cussion on  page  187  and  to  the  note  on  page  254.  This  process  is 
of  special  importance  in  the  case  of  platinized  platinum  electrodes, 
because  they  dissolve  large  quantities  of  gases,  and,  further,  because 
a  state  of  equilibrium  is  established  in  a  short  time.  At  a  platinized 
ferri-ferro  electrode,  for  example,  the  following  equilibrium  equa- 
tions must  be  satisfied  :  — 


2Fe"  +    2  ^>  2  Fe"'  +  O". 
2 

If  the  tri-  and  bivalent  iron  ions  are  of  normal  concentration  in  the 
solution,  then  the  potential-difference,  — 

Ic  electrode  -  electrolyte  =  +  0.46  Volt. 

1  See  also  Fredenhagen,  Ztschr.  anorg.  Chem.,  29,  396  (1902.) 


264  A   TEXT-BOOK   OF   ELECTRO-CHEMISTRY 

It  follows  from  this  that,  at  a  given  concentration  of  hydrogen  and 
oxygen  ions,  the  concentrations  of  the  hydrogen  and  the  oxygen  in 
the  electrode  may  be  calculated.  The  latter  must,  naturally,  be 
changed  by  a  change  in  the  concentration  of  the  hydrogen  and  oxy- 
gen ions  if  that  of  the  iron  ions  remains  unchanged.  A  short  con- 
sideration shows  that  to  a  higher  charge  of  oxygen  there  always 
corresponds  a  lower  one  of  hydrogen,  and  conversely.  Now  it  is 
evident  that  when  the  concentration  of  the  gas  in  the  electrode  be- 
comes too  great,  it  escapes  from  the  electrode.  Assuming  that  this 
takes  place  if  the  hydrogen  or  oxygen  exerts  a  pressure  of  one  atmos- 
phere, then  it  may  be  stated  that  every  oxidizing  agent  for  which 

2c  electrode -electrolyte  >  0.94  Volt, 

or,  what  is  the  same  thing, 

Eft  electrode  -electrolyte  >  1-22  VOltS, 

must  cause  the  evolution  of  oxygen  from  a  solution  which  is  normal 
in  respect  to  hydrogen  ions.  This  action  must,  moreover,  continue 
until  the  concentrations  involved  have  been  so  diminished  as  to 
lower  the  potential-difference  to  the  value  0.94  or  1.22  volts,  accord- 
ing to  the  standard  of  reference  adopted.  On  the  other  hand,  a  re- 
ducing agent  for  which  the  potential-difference  FC  or  FA  is  less  than 
—0.283  or  0.00  volt  respectively,  will  cause  hydrogen  to  be  evolved 
from  a  solution  of  hydrogen  ions  of  normal  concentration.  Thus  it 
is  seen  that  oxidizing  and  reducing  agents  in  aqueous  solutions  are 
relatively  stable,  and  capable  of  measurement  only  within  narrow 
limits.  Outside  these  limits  only  states  in  transition  exist,  and 
therefore  the  deduced  equations  are  no  longer  applicable.  This  is 
true,  for  instance,  of  solutions  of  persulfates  which  break  down 
into  sulfates  with  the  evolution  of  oxygen.  Only  when  the  per- 
sulfate  concentration  becomes  very  slight  is  the  potential-differ- 
ence corresponding  to  its  relative  stability  reached.  Eelative 
stability  only  can  be  spoken  of  because  all  oxidizing  and  reducing 
agents  undergo  such  a  change  with  hydrogen  and  oxygen  ions  (and 
consequently  with  the  corresponding  charges  of  gases  on  the  elec- 
trode) that  their  electrode  potential-differences  always  approach  that 
value  corresponding  to  the  atmospheric  oxygen.  Since  this  oxygen 
is  present  in  an  inexhaustible  quantity,  its  concentration  remains 
constant.  The  iron  electrode  mentioned  above  is  in  stable  equilib- 
rium in  the  air  only  when  in  a  solution  of  such  a  concentration  in 
respect  to  the  oxygen  (or  hydroxyl)  ions  that  the  electrode  of  atmos- 
pheric oxygen  in  it  also  produces  a  potential-difference  of  0.46  volt. 


ELECTROMOTIVE  FORCE  265 

The  assumption  is  here  made  that  the  existing  hydrogen  concentra- 
tion in  the  electrode  remains  unchanged.  Since,  strictly  speaking, 
this  would  only  be  the  case  when  the  corresponding  pressure  of 
hydrogen  exists  in  the  atmosphere,  which  certainly  is  not  the  case, 
the  conclusion  is  now  reached  that  a  state  of  complete  equilibrium 
is  never  attained.  However,  since  as  long  as  the  pressures  of  the 
gases  do  not  exceed  one  atmosphere  they  diffuse  from  the  electrode 
into  the  surroundings  very  slowly,  it  may  be  assumed  in  practice 
that,  below  this  limit,  the  relations  may  be  calculated. 

Another  important  result  may  be  obtained  from  these  considera- 
tions. If  for  a  reducing  agent, 

£A  electrode -electrolyte  <   0.00  Volt, 

it  will  no  longer  be  stable  in  a  1  normal  solution  of  hydrogen  ions, 
but  will  be  stable  in  a  solution  containing  less  hydrogen  ions,  as, 
for  example,  in  a  solution  containing  hydroxyl  ions.  The  lower  the 
hydrogen  ion  concentration,  the  greater  (counting  negatively)  will 
be  the  potential-difference  between  the  hydrogen  under  atmospheric 
pressure  and  the  solution,  and  the  greater  can  also  be  that  between 
the  reducing  agent  and  the  solution  without  causing  hydrogen  to  be 
evolved.  The  less  noble  metals,  such  as  iron,  furnish  the  simplest 
illustration  of  this  behavior.  In  a  1  normal  solution  of  ferrous 
ions,  which  is  neutral  and  therefore  contains  but  few  hydrogen  ions, 
iron  does  not  evolve  hydrogen.  On  the  other  hand,  if  the  solution 
is  acid  and  therefore  contains  many  hydrogen  ions,  the  iron  evolves 
hydrogen  immediately. 

An  analogous  discussion  may  be  applied  to  the  case  of  oxidizing 
agents,  or  substances  producing  high  positive  potential-differences. 
They  are  more  stable  and  evolve  oxygen  less  energetically  and  after 
a  longer  time  in  acid  than  in  alkali  solutions. 

In  the  previous  discussion  it  was  assumed  that  the  potential-dif- 
ference in  the  case  of  such  oxidizing  or  reducing  agents  as  a  ferri- 
ferro  solution,  the  changes  of  which  do  not  involve  hydrogen  or 
hydroxyl  ions,  is  independent  of  the  concentration  of  these  ions,  i.e. 
is  the  same  in  acid  or  alkali  if  the  concentration  of  the  ions  of  the 
oxidizing  or  reducing  substance  is  not  changed.  Within  certain 
limits,  experimental  measurements  have  confirmed  this  assump- 
tion. The  magnitude  of  the  concentration  of  the  gases  hydrogen  and 
oxygen  on  the  electrodes  naturally  changes,  as  already  explained, 
corresponding  to  the  changes  in  the  concentrations  of  the  hydrogen 
and  oxygen  ions. 

If  there  is  a  possibility  of  further  reactions  taking  place  at  the 


266  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

electrodes,  as  would  be  the  case,  for  example,  if  iodine  be  added, 
then  in  this  case,  when  equilibrium  is  again  established,  the  poten- 
tial-difference between  the  iodine  and  iodine  ions  must  be  equal  to 
that  just  considered  above.  If  the  electrolytic  potential-difference 
for  the  individual  reactions  be  known,  then  very  interesting  calcu- 
lations may  be  carried  out.  For  example,  we  may  calculate  the 
ratio  of  ferrous  to  ferric  ions  which  may  exist  in  a  normal  solution 
of  iodine  ions  which  is  saturated  with  iodine.1 

If  it  is  so  desired,  all  galvanic  cells,  especially  those  with  plati- 
nized electrodes,  may,  therefore,  be  considered  as  hydrogen  and 
oxygen  concentration  cells.  It  is  not  possible  to  say  with  certainty 
just  how  in  the  individual  cases  the  electric  current  comes  into 
existence.  It  is,  in  all  probability,  different  in  different  cases.  In 
the  case  of  the  ferri-ferro  electrode  it  may  be  assumed,  as  has  been 
done  in  the  preceding  pages,  that  the  current  results  from  the  direct 
transformation  of  ferric  into  ferrous  ions,  but  it  also  seems  permis- 
sible to  assume  that  the  current,  or  a  part  of  it,  results  from  such  a 
reaction  between  the  ferric  and  hydroxyl  (or  oxygen)  ions  as  is  rep- 
resented by  the  equations  given  on  page  263.  As  a  result  of  this 
reaction,  the  electrode  may  become  laden  with  hydrogen,  and  there- 
upon become  electromotively  active.  In  the  case  of  the  oxidation 
of  thiosulfate  to  tetrathionate  according  to  the  equation, 


it  has  been  shown  by  Thatcher  2  to  be  very  probable  that  the  process 
only  takes  place  through  the  agency  of  oxygen.  Likewise  in  the 
case  of  organic  oxidizing  agents,  for  example  chinone,  which  are 
not  measurably  ionized,  the  above  assumption  seems  plausible.  In 
an  analogous  manner,  through  a  reaction  taking  place  at  the  elec- 
trode by  which  a  reducing  is  transformed  into  an  oxidizing  sub- 
stance, e.g.  ferrous  into  ferric  ions,  the  electrode  may  become  laden 
with  hydrogen,  and  then  exhibit  an  electromotive  force.  In  the 
case  of  the  metal  electrodes  we  will  assume  that  the  current  is  not 
produced  by  such  an  indirect  process,  but  by  the  direct  passage  of 
the  metal  into  the  ionized  state,  although  opposition  to  this  view 
has  already  become  strong. 

There  are  many  metals  which,  upon  being  dissolved  electrolyti- 
cally,  are  capable  of  forming  more  than  one  kind  of  ions.  This  fact 
raises  a  question  as  to  the  nature  of  the  process  of  solution  in  such 

1  For  further  particulars,  see  Abegg,  Ztschr.  Electrochem.,  9,  569  (1903). 

2  Ztschr.  phys.  Chem.,  47,  641  (1904). 


ELECTROMOTIVE  FORCE  267 

cases.1  Now  the  metals  must  dissolve  in  such  a  manner  that  the 
potential-differences  between  the  electrode  and  the  various  ions  shall 
be  the  same.  The  relation  between  the  concentrations  of  the  ions 
being  formed  is  thereby  determined.  If  another  substance,  which 
forms  a  complex  compound  with  one  kind  of  ions,  be  added  to  the 
solution,  it  is  at  once  evident  that  the  valence  with  which  the  metal 
goes  into  solution  will  be  more  or  less  changed  in  favor  of  the  ion 
thus  constantly  removed  to  form  the  complex  compound.  Undoubt- 
edly complications  often  appear  during  the  solution  of  metals. 
They  will  be  considered  further  in  the  section  on  the  passive 
state. 

ELECTROMOTIVE   FORCE   AND  CHEMICAL  EQUILIBRIUM 

When  an  electromotively  active  reaction  takes  place  at  an  elec- 
trode, and  all  effective  concentrations  are  equal  to  unity,  the 
measured  value  of  the  potential-difference  of  this  reaction  has  been 
called  its  "  electrolytic  potential "  (see  page  253).  Absolute  values 
of  the  "  electrolytic  potentials  "  cannot  be  obtained  with  certainty  at 
present.  The  question  now  arises  whether  or  not  such  values  may 
be  calculated  directly  from  purely  chemical  data. 

In  order  to  calculate  the  value  of  the  electrolytic  potential,  it  is 
only  necessary  to  know  the  maximum  quantity  of  work  obtainable 
when,  by  means  of  anon-electrical,  isothermal,  reversible  process,  the 
substances  involved  on  one  side  of  the  reaction  equation  at  unit  con- 
centration are  transformed  into  the  substances  involved  on  the 
other,  likewise  at  unit  concentration.  If  now  the  transformation  be 
imagined  to  take  place  electrically,  the  maximum  work  obtainable  is 

We  =  VQF. 

Since  the  maximum  quantity  of  work  is,  according  to  the  second  law 
of  energetics,  the  same  whatever  the  process  used, 

Wm=  TFe=VQF, 

F  =  ^. 

VQ 

The  value  of  W  can,  in  the  case  of  gases  and  dissolved  substances  in 
dilute  solutions,  be  calculated. 
Consider  the  system, 

aA  +  bB—  +  VQ  (+)  ^-dD+  eE  ••• 

1  Le  Blanc,  Ztschr.  Electrochem.,  9,  635  (1903)  ;  Abegg-Skukoff,  Ztschr. 
Electrochem.,  12,  457  (1906). 


268  A   TEXT-BOOK   OF   ELECTRO-CHEMISTRY 

in  equilibrium,  that  is  to  say,  under  such  conditions  of  concentration 
that  no  work  is  required  to  carry  out  the  process  in  either  direction. 
Further,  let  these  concentrations  be  represented  by 

O'  n  i       n  '    n  ' 
A)    ^  £  )  '"    ^  D  )     <->  g  )  •") 

and  the  number  of  mols  of  the  substances  involved  by 

a,  6,..-  d,e,—  , 

respectively  (see  page  253).  Then  according  to  the  mass  action  law, 
the  following  relation  exists  between  the  quantities  of  the  substances 
entering  the  reaction  :  — 

Co  I      ^    (~*1b  I 
A       X    ^B      '"  _    JTI 


where  KJ  is  the  equilibrium  constant. 

In  order  to  calculate  the  maximum  work  W  of  the  process,  we  may 
proceed  as  follows  :  — 

1.  With  the  aid  of  the  simple  gas  laws  which  apply  to  dissolved 
substances  (see  page  168),  the  work  expended  or  gained  in  bringing  the 
given  number  of  mols  of  the  substances  on  one  side  of  the  above 
reaction  equation  from,  the  concentration  unity  to  the  concentrations 
CA',  CB',  •"  may  be  calculated. 

2.  Under  equilibrium  conditions,  these  substances   at  the  above 
concentrations  may  be  transformed  into  the  substances  on  the  other 
side   of  the  reaction  equation  at  the  concentrations  CD\  CE',  •••, 
without  the  expenditure  of  work. 

3.  Finally,  the  quantity  of  work  involved  when  the  concentrations 
of  the  latter  substances  are  changed  from  CD',  CE\  •••  to  unity  may 
be  calculated. 

If  T  is  the  room  temperature  and  W  the  maximum  work  of  this  pro- 
cess, the  following  equation  is  obtained  from  the  above  calculations.1 


Therefore  the  absolute  value  of  the  "  electrolytic  potential  "  is  given 
by  the  equation, 


By  combining  this  equation  with  that  given  on  page  253,  the  follow- 
ing general  expression  is  obtained  :  — 

1For  further  particulars  see  Nernst,   Theoret.  Chem.,  4th  edition,  p.  630 
(1903). 


ELECTROMOTIVE   FORCE  269 


F  (absolute)  =  —  fin  °f  x°*  '"  +  In 
'' 


or  F  (absolute)  =  —  An  A7  +  In 


CX  ) 


where  CA,  CB,  •-  CD,  CM,  •••  represent  any  concentrations  of  the 
substances  involved. 

The  value  of  ^"e,  the  equilibrium  constant  of  the  single  reaction 
which  takes  place  at  one  electrode,  cannot,  however,  be  experimen- 
tally determined,  for  a  chemical  reaction  always  consists  of  an  oxida- 
tion and  a  simultaneous  reduction  ;  never  of  one  of  them  alone.  By 
chemical  methods,  it  is  only  possible  to  determine,  in  a  given  experi- 
ment, the  equilibrium  constant  of  the  total  reaction  taking  place  at 
the  two  electrodes.  It  is,  therefore,  not  possible  by  means  of  deter- 
minations of  equilibrium  constants  to  obtain  a  knowledge  of  the 
values  of  the  potential-differences  of  single  electrodes.  However, 
with  the  help  of  such  determinations,  and  a  knowledge  of  the  con- 
centrations of  the  substances  reacting  at  the  electrodes,  it  is  possible 
to  calculate  the  electromotive  force  of  the  cell,  which  is,  if  the  po- 
tential-difference between  liquids  be  disregarded,  equal  to  the  sum  of 
the  two  single  potential-differences.  This  may  be  done  with  the 
help  of  the  equation,  * 


A"     —  I      AJ.J.     -J-^f      T^    M.M.L 1  • 

v«  V          c;  x  oi  -A 

in  which  JTe  is  the  equilibrium  constant  of  the  total  reaction  taking 
place  in  the  cell,  F  is  the  electromotive  force  of  the  entire  cell,  and 
the  terms  after  the  logarithm  sign  are  the  concentrations  of  the 
substances  which  react  at  the  two  electrodes  respectively. 

In  this  connection  it  should  be  remembered  that  the  electromotive 
force  of  any  galvanic  cell  may  be  calculated  by  a  second  method  with 
the  aid  of  the  heat  of  reaction  Q,  and  the  temperature  coefficient  of 

the  potential-difference  — ^.  The  equation  is  that  formulated  by 
Helmholtz  (see  page  173)  :  — 


The  former  equation,  first  put  forward  by  van't  Hoff  in  the  year 
1886,  has  recently,  at  the  instance  of  Bredig,  been  tested  experimen- 
tally by  Knupffer.1  The  results  obtained  will  now  be  considered. 

1  Ztschr.  phys.  Chem.,  26,  255  (1898);  also,  Ztschr.  Elektrochem.,  4, 544  (1898). 


270  A   TEXT-BOOK  OF   ELECTRO-CHEMISTRY 

The  double  reversible  chemical  transformation, 

T1C1  +  KSCN  2  T1SCN  +    KC1, 
solid       dissolved          solid          dissolved 

was  investigated.  Since  the  transformation  is  independent  of  the 
quantity  of  the  solid  salts,  and  since  the  concentrations  of  the  latter 
may  be  regarded  as  constant,  it  is  only  necessary  to  consider  the  sub- 
stances in  solution.  It  is,  moreover,  assumed  that  the  solutions  are 
dilute  and  that  the  dissolved  substances  are  completely  dissociated, 
i.e.  are  present  in  solution  in  the  form  of  potassium,  sulfocyanate, 
thallium,  and  chlorine  ions.  The  potassium  ions  take  no  part  in  the 
reaction.  The  equilibrium  conditions  are,  then,  given  by  the  equa- 
tion, 

CTI  X  Ccr  _   @c\'  __  g  ^ 

GTI*  X  CSCN'      GSCN' 

Attention  is  called  to  the  fact  that 


is  the  solubility  product  of  a  saturated  thallium  chloride  solution, 
and  that  CTI-  X  CSCN-  =  Sf 

is  that  of  a  saturated  solution  of  thallium  sulfocyanate.  Hence  the 
equilibrium  constant  is  in  this  case  equal  to  the  ratio  of  the  two 
solubility  products  and  may  be  calculated  from  these  quantities.  It 
was,  in  fact,  determined  by  ascertaining  the  concentrations  of  the 
chlorine  and  sulfocyanate  ions  in  solutions  formed  by  shaking  a  solu- 
tion of  potassium  chloride  with  solid  thallium  sulfocyanate,  and  by 
shaking  a  solution  of  potassium  sulfocyanate  with  solid  thallium 
chloride.  The  following  average  results  were  obtained  for  this  re- 
action :  — 

TEMPERATURE  (<°)  EQUILIBRIUM  CONSTANT 

0.8°  1.74 

20.0°  1.24 

39.9°  0.85 

Using  these  values  of  the  equilibrium  constant,  it  is  possible  to 
calculate,  for  any  known  concentrations  of  chlorine  and  sulfocyanate 
ions,  the  values  of  the  electromotive  force  of  this  process  at  these 
temperatures.  By  placing 


ELECTROMOTIVE   FORCE  271 

in  the  equation  given  on  page  269,  the  following  expression  is  ob- 
tained :  — 


In  order  to  be  able  to  measure  directly  this  electromotive  force,  it  is 
accessary  to  devise  a  cell  by  means  of  which  this  reaction  may  be 
made  to  produce  an  electric  current.  Such  a  cell  is  the  following 
combination  :  — 

Thallium  amalgam  —  KC1  solution  sat.  with  T1C1-  -----  -,  ^ 

Thallium  amalgam  -  KSCN  solution  sat.  with  T1SCN.-.1  ' 

If,  when  this  cell  is  in  action,  the  positive  electric  current  flows  in 
the  cell  from  the  upper  to  the  lower  thallium  amalgam  in  the  above 
scheme,  thallium  and  sulfocyanate  ions  are  formed  while  simul- 
taneously thallium  and  chlorine  ions  disappear.  Hence  only  the 
chlorine  and  sulfocyanate  concentrations  are  changed.  The  electro- 
motive force  of  the  cell  must,  therefore,  depend  upon  the  ratio  of 
these  two  concentrations  to  each  other. 

The  values  of  the  electromotive  force  found  by  experiment  agree 
well  with  those  calculated  with  the  aid  of  the  equilibrium  constants, 
as  may  be  seen  from  the  following  table  :  — 

ELECTROMOTIVE  FORCE 
TEMPERATURE  Calculated  Found 

0.8°  17.1  17.5  millivolts 

20.0°  9.8  10.5  millivolts 

39.9°  0.6  1.0  millivolt 

It  may  be  remarked,  further,  that  this  cell  can  also  be  considered 
as  a  concentration  cell  in  respect  to  the  thallium  ions,  and  that  its 
electromotive  force  can  also  be  calculated  by  means  of  the  equation 
applying  to  such  cells. 

One  further  interesting  relation  is  shown  by  the  equation  given 
above.  If  a  is  made  equal  to  Ktt  i.e.  if  equilibrium  concentra- 
tions are  maintained,  then  the  electromotive  force  of  the  cell  is 
equal  to  zero.  This  follows  from  the  fact  that,  when  chemical 
equilibrium  exists  in  a  cell,  electrical  equilibrium  must  also  exist. 
Utilizing  this  fact,  the  appearance  of  a  state  of  equilibrium  may  be 
shown  by  electrical  measurements.  Thus  Cohen  l  determined  transi- 
tion points  by  means  of  measurements  of  electromotive  force.  Zinc 
sulphate  crystallizes  at  room  temperature  with  seven  molecules  of 

i  Ztschr.  phys.  Chem.,  14,  53  and  635  (1894). 


272  A   TEXT-BOOK  OF   ELECTRO-CHEMISTRY 

water,  while  at  a  somewhat  higher  temperature  it  crystallizes  with 
six  molecules.     Hence  with  the  combination, 


Zn  —  ZnSO4  •  7  H20  in  contact  with  the  solid  salt- 
Zn  —  ZnS04  •  6  H2O  in  contact  with  solid  salt 


which  is  a  concentration  cell  (or  in  this  case  a  transition  cell),  an 
electric  current  may  be  obtained  because  the  two  hydrates  are  not 
equally  soluble.  Its  construction  is  conditioned  by  the  fact  that 
below  the  transition  temperature  the  metastable  hydrated  salt, 
ZnS04  •  6  H2O,  may  exist  for  some  time.  This  condition  can,  how- 
ever, be  avoided  by  an  artifice.  If  the  temperature  of  such  a  cell  be 
varied,  so  slowly  that  the  solution  is  always  saturated,  to  the  transi- 
tion temperature,  the  electromotive  force  decreases  and  finally  at 
this  temperature  becomes  equal  to  zero,  since  here  the  solubility 
curves  of  the  two  hydrated  salts  intersect  each  other.  From  what 
has  already  been  stated  in  reference  to  concentration  cells,  evidently 
the  relations  existing  in  this  cell  may  be  calculated. 
The  reaction, 

Metal  oxide  ^  metal  +  oxygen, 

and  also  the  reaction, 

Metal  halide  ^±  metal  -f-  halogen, 

forms  an  especially  simple  case.     Here  the  following  equation  holds, 

W=ETlupd, 

where  pd  represents  the  dissociation  tension  or  pressure  of  the  metal 
oxide  at  the  temperature  T,1  for  it  alone  determines  the  equilibrium. 
In  this  equation  W  represents  the  work  obtainable  when  one  mol  of 
oxygen  passes  from  a  pressure  pd  atmospheres  to  a  pressure  of  one 
atmosphere.  It  may  be  obtained  in  the  form  of  electrical  energy 
with  the  aid  of  the  cell, 

Metal  —  solution  of  metal  oxide  (sat.)  —  oxygen  (atm.  pressure). 

When  one  mol  of  oxygen  is  transformed  in  this  cell,  the  electrical 
work, 

TF.  =  4FQ. 

Hence  we  have  the  following  equation  :  — 


1  Rothmund,  Ztschr.  phys.  Chem.,  32,  69  (1899);   and  Lewis,  Ztschr.  phys. 
Chem.,  55,  449  (1906). 


ELECTROMOTIVE   FORCE  273 

Therefore,  the  value  of  F  being  known,  that  of  pd  may  be  calculated. 
This  cell  may  also  be  considered  as  a  concentration  cell  in  respect  to 
oxygen. 

The  investigation  of  Luther  and  Sammet  l  furnishes  an  example 
of  a  somewhat  more  complicated  relation  between  the  electromotive 
force  and  the  equilibrium  constant.  The  equilibrium  constant  of 

the  reaction, 

6  H-  +  KV  +  5  i'^s  i2  +  3  H20, 


was  determined  chemically,  giving  the  following  :  — 

Ke  (25o)  =  (H-)6  x  (I(V)  X  (iy  =  2.8  (+  0.3)  x  10-". 
(^-2) 

The  above  reaction  may  now  be  considered  to  be  made  up  of  the 
following  individual  processes  :  — 

(a) 
(6) 
(c) 

A  summation  in  the  usual  manner  of  the  members  on  either  side  of 
the  ~^~  sign  of  these  equations  gives  the  above  original  reaction 
equation. 

If  now  all  three  processes  exist  in  equilibrium  in  a  mixture,  and 
if  a  reversible  electrode  for  each  process  be  placed  in  the  mixture, 
then  it  follows  from  what  has  been  said  in  the  last  two  sections  that 
the  three  potential-differences  between  the  respective  electrodes  and 
the  solution  must  be  equal  to  each  other.  Under  these  circum- 
stances these  potential-differences  will  be  represented  by  the  follow- 
ing equations  :  — 

(a)  (a) 

F  F  A-RT  i      (H')12  x  (I(V)a 

-  electrode  -  electrolyte  =  ^0  +  -  In    *  -  «  -      -  ^—  J 


F  -»    ,  in  (H')6  X  (IPs')  . 

-  electrode  -  electrolyte  —  H)  T  -  ±n  ^-         —  —  *-  , 


(«)  (c) 

F  _F      RT  -.     (L,). 

-  electrode  -  electrolyte  —  -0    »      n  Q  /Tf\2  ' 


1  Ztschr.  phys.  Chem.,  53,  641  (1905)  ;  Ztschr.  Electrochem.,  11,  293  (1905). 
x 


274 


A   TEXT-BOOK   OF   ELECTRO-CHEMISTRY 


and  when  the  potential-differences  are  equal  we  obtain  the  follow- 
ing:— 

(6)    (a) 


'  0) 

-Zo  =  ^fln£T; 

I    (a) 


For  process  (a)  it  was  possible  to  obtain  a  reversible  platinum 
electrode.  The  concentrations  of  H',  I03',  and  I2  were  found  to  be 
of  considerable  magnitude  and  also  measurable.  Hence  it  was  pos- 
sible to  determine^  'and  therefore  also^  'and  ^  f 

lo  F0  F0. 

In  an  analogous  manner  the  reaction, 

6  H'+  Br03'  -f  5  Br' ^±3  Br2  +  3  H20, 

was  investigated.  It  was  found  possible  to  calculate  the  corre- 
sponding values  for  chlorine.  The  following  results  referred  to  the 
calomel  cell  were  obtained :  — 


FQ  electrode  •<—  electrolyte 

IODINE 

BROMINE 

CHLORINE 

Process  (<z)   

0894 

1.186 

1.25 

Process  (&)   

0802 

1  138 

1.23 

Process  (c)    .    .    .    .    .    . 

0345 

0812 

1.12 

In  the  case  of  bromine  and  of  iodine  there  exists  a  considerable 
potential-difference  between  the  liquids.  By  means  of  an  artifice 
this  has  been  made  calculable,  thus  permitting  it  to  be  taken  into 
consideration  in  calculating  the  above  values.  The  temperature  of 
the  measurements  was  25°. 

It  being  known  that  at  the  transformation  temperature,  or,  more 
generally  speaking,  at  the  point  of  equilibrium  of  two  systems,  the 
potential-difference  is  equal  to  zero,  it  may  at  once  be  concluded 
that  no  potential-difference  exists  between  a  solid  and  a  fused  metal 
at  its  melting  point.  It  is  impossible,  therefore,  to  obtain  an  electric 
current  from  a  cell  composed  of  an  electrolyte,  and  of  a  fused  and  a 
solid  electrode  of  the  same  substance  at  this  temperature.  From 


ELECTROMOTIVE  FORCE  275 

this  it  is  evident  that  the  heat  of  fusion,  no  more  than  the  heat  of 
solution  (see  also  page  227)  can  be  considered  exclusively  as  the 
direct  source  of  the  electrical  energy.  This  conclusion  has  been 
confirmed  by  the  results  of  experiment. *  If  such  a  cell  be  placed  in 
surroundings  of  a  temperature  other  than  the  melting  point,  whereby 
either  the  liquid  or  the  solid  phase  must  become  unstable,  naturally 
an  electric  current  is  obtained  because  the  two  phases  are  no  longer 
in  equilibrium  ;  but  the  one  is  capable  of  undergoing  transformation 
into  the  other  with  the  simultaneous  production  of  free  energy. 

VELOCITY  OF  IONIZATION.    PASSIVITY.    CATALYTIC 
INFLUENCE 

Up  to  the  present  the  velocity  of  the  passage  of  a  substance  to  and 
from  the  ionized  state  has  been  left  entirely  out  of  consideration  under 
the  tacit  assumption  that,  in  comparison  with  the  velocities  usually 
measured,  it  is  infinitely  great.  In  the  case  of  the  Daniell  cell,  for 
example,  at  a  constant  temperature,  the  electromotive  force  is  depend- 
ent only  on  the  concentrations  of  the  two  solutions.  Constant  prop- 
erties are  ascribed  to  the  zinc  (which  furnishes  the  ions)  which  are 
also  independent  of  the  strength  of  the  electric  current.  It  may 
now  be  questioned  whether  there  are  not  cases  in  which  the  velocity 
of  the  formation  of  ions  is  no  longer ,  infinitely  great,  but  possesses 
very  different  values  under  different  circumstances.  What  would 
happen  in  the  case  of  the  Daniell  cell  if  suddenly  the  velocity  of 
the  formation  of  zinc  ions  should  fall  to  zero  ?  In  answer  to  this 
question  it  may  be  stated  that  the  zinc  would  then  behave  like 
a  noble  metal  and  that  the  cell  would  no  longer  of  itself  furnish  an 
electric  current.  If,  furthermore,  with  the  aid  of  an  independent 
electromotive  force,  an  electric  current  should  be  sent  through  the 
cell  in  the  direction  of  the  current  of  an  ordinary  Daniell  cell,  oxy- 
gen would  be  evolved  at  the  zinc  electrode. 

In  general  there  are  a  number  of  possible  processes  which  may 
take  place  at  an  electrode  upon  the  passage  of  an  electric  current, 
and  of  these  processes,  that  one  takes  place  which  gives  rise  to  the 
highest  electromotive  force.  Here  again  it  is  assumed  that  the  veloc- 
ity of  ionization  is  infinitely  great.  If  this  velocity  is  not  suffi- 
ciently great,  the  above  principle  becomes  invalid. 

It  sometimes  happens  that  a  base  metal  which  under  ordinary 
circumstances  is  dissolved  as  required  by  its  valence  and  Para- 
day's  law,  under  other  conditions  behaves  like  a  noble  metal 

i  Ztschr.  phys.  Chem.,  10,  459  (1892). 


276  A   TEXT-BOOK   OF  ELECTRO-CHEMISTRY 

This  behavior  is  called  passivity.  It  was  first  observed  with  iron 
at  the  end  of  the  eighteenth  century.  In  concentrated  nitric  acid 
iron  loses  the  power  of  dissolving  with  the  evolution  of  hydrogen 
which  it  possesses  in  dilute  acids.  Even  when  used  as  an  anode  in 
dilute  nitric  acid  it  does  not  go  into  solution,  but  instead  permits  an 
evolution  of  oxygen.  Recently  it  has  been  found  that  this  phe- 
nomenon of  passivity  is  of  frequent  occurrence,  occurring  with  iron, 
nickel,  and  other  metals  in  alkali  solutions,  with  nickel  also  when 
it  is  used  as  an  anode  at  ordinary  temperatures  in  salt  solutions 
which  are  neutral,  or  acid  with  nitric  or  sulfuric  acid. 

Until  recently,  the  phenomena  of  passivity  were  explained  on  the 
assumption  of  the  existence  of  a  film  of  oxide  covering  the  metal  and 
protecting  it  mechanically  from  corrosion.  There  is  no  doubt  but 
that  this  explanation  is  a  satisfactory  one  for  a  large  number  of 
cases.  This  is  sometimes  evident  from  the  appearance  alone.  For 
example,  lead  when  used  as  an  anode  in  a  pure  sulfuric  or  chromic 
acid  solution  with  a  sufficiently  small  current  density  is  insoluble 
and  becomes  covered  with  a  visible  layer  of  lead  sulfate  or  peroxide 
at  which  oxygen  is  evolved.  Analogous  behavior  is  always  observed 
when  a  salt,  the  anion  of  which  forms  a  difficultly  soluble  compound 
with  the  anode  metal,  is  used  as  the  electrolyte. 

It  is  a  remarkable  fact  that  the  anode  metal  is  easily  dissolved 
when,  besides  a  salt  of  the  above  description,  the  electrolyte  contains 
another  one  in  excess  which  is  indifferent  and  which  furnishes  an 
anion  which  forms  an  easily  soluble  salt  with  the  anode  metal. 
This  behavior  is  utilized  technically  in  the  preparation  of  difficultly 
soluble  compounds  (Luckow's  process).1  For  example,  lead,  when 
used  as  an  anode  in  a  solution  of  sodium  chr ornate  and  sodium 
chlorate,  dissolves  easily,  and  a  beautiful  precipitate  of  lead  chro- 
mate  is  formed  which  rolls  from  the  electrode,  leaving  it  still  bright. 
This  is  explained  by  assuming  that,  due  to  the  action  of  the  indiffer- 
ent ions  in  the .  mixed  solution,  a  liquid  layer  free  from  chr  ornate 
ions  is  formed  directly  at  the  surface  of  the  electrode  soon  after 
the  electrolysis  is  started.  The  adhesion  of  the  precipitate  to  the 
electrode  is  thus  prevented.  Hence  only  at  the  beginning  of  the 
electrolysis  can  a  precipitate  of  lead  chromate  be  formed  directly  on 
the  anode,  and  this  precipitate  does  not  protect  the  electrode,  for 
a  covering  impenetrable  to  ions  can  only  be  formed  when  it  can  be 
continually  patched  or  repaired. 

After  the  above  presentation  of  the  subject,  it  would  be  justifiable 

1  Le  Blanc  and  Bindschedler,  Isenburg,  Just ;  Ztschr.  Elelctrochem.,  8,  255 
(1902);  9,  275  and  547  (1903). 


ELECTROMOTIVE  FORCE  277 

for  one  to  expect  that,  if  the  passivity  of  a  metal  in  an  electrolyte 
is  governed  by  the  formation  of  a  precipitate,  the  addition  of  a 
second  electrolyte  in  which  the  same  metal  as  an  anode  dissolves, 
forming  a  soluble  compound,  would  overcome  the  passivity  and 
cause  the  solution  of  the  metal  with  the  simultaneous  formation  of 
a  precipitate  which  would  fall  from  the  electrode,  as  in  the  case 
of  the  lead  chromate.1  This  holds  for  individual  cases,  as  for 
example  nickel  and  iron  in  alkali  solutions,  but  not  in  others.  For 
instance,  although  nickel  as  an  anode  dissolves  in  sodium  nitrate, 
upon  the  addition  of  sodium  chloride  no  precipitate  is  formed.  It 
seems  scarcely  possible  to  explain  this  case  of  passivity  in  the 
above  manner,  i.e.  on  the  assumption  of  the  formation  on  the 
originally  active  metal  of  a  protective  coating.  Some  kind  of  an 
insoluble  oxide  or  other  compound  may  gradually  form.  It  can- 
not, however -,  be  the  cause  of  the  passive  state  of  the  metal,  but,  on  the 
other  hand,  must  be  the  result  of  previously  existing  passivity.  The 
same  can  be  said  of  a  film  or  coating  of  a  gas  which  may  appear. 
Up  to  the  present,  the  optical  investigation  of  the  electrode  surface 
has  not  led  to  a  conclusive  result.  It  would  only  be  of  decisive  sig- 
nificance if  it  furnished  certain  proof  that  in  individual  cases  of  pas- 
sivity no  oxide  layer  or  coating  is  formed.  A  proof  of  the  presence  of 
such  a  coating,  on  the  other  hand,  could  not,  as  already  emphasized, 
be  considered  as  a  conclusive  result  in  the  opposite  direction. 

The  above  discussion  brings  us  to  the  idea  already  indicated,  that 
here  we  are  often  dealing  with  nothing  more  than  the  phenomenon 
of  reaction  velocity.  It  is  well  known  that  the  velocity  of  a  large 
number  of  reactions  is  not  only  greatly  changed  by  temperature 
changes,  but  also  by  the  addition  of  substances  which  are  apparently 
inert.  Furthermore,  it  is  known  that  a  large  number  of  reactions 
proceed  with  such  a  moderate  velocity  that  they  can  be  easily  fol- 
lowed. It  should  not  surprise  us  especially,  therefore,  to  know  that 
the  velocity  with  which  a  metal  goes  from  the  elementary  state  to 
the  ionic  state  is  not  always  very  great.  This  tracing  back  of  real 
passivity  to  an  exceedingly  small  ionization  velocity  of  the  metal 
is  a  gain  in  that  it  uncovers  the  real  character  of  this  phenomenon. 
It  is  then  only  a  special,  if  also  an  especially  interesting,  case  of 
reaction  velocity.2 

Platinum  as  an  anode  does  not  dissolve  in  a  solution  of  potassium 

1  Le  Blanc  and  Levi,  Boltzmann-Festschrift,  1904,  and  Ztschr.  EleJctrochem. , 
11,  9  (1905). 

2  Less  general  conceptions  of  passivity  are  given  by  W.  Miiller,  Ztschr.  Elek- 
trochem.,  11,  755  and  823,  and  by  O.  Sackur,  in  the  same  volume,  p.  841  (1905). 


278  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

cyanide,  but  according  to  F.  Glaser,1  it  dissolves  like  a  base 
metal  in  the  same  solution  without  the  aid  of  the  electric  current, 
although  very  slowly,  accompanied  by  the  evolution  of  hydrogen. 
This  must  be  considered  as  a  case  of  true  passivity. 

The  investigations  of  Hittorf  on  chromium 2  may  be  interpreted  in 
a  similar  manner.  According  to  the  choice  of  solvent,  tempera- 
ture, etc.,  the  chromium  is  dissolved  at  the  anode  in  a  di-,  tri-,  or 
hexavalent  state.  In  dilute  hydrochloric  acid,  for  example,  the 
chromium  dissolves  at  moderate  temperatures  in  the  divalent  state. 
If,  however,  solutions  of  the  alkali  sulfates  be  subjected  to  elec- 
trolysis at  100°  t,  using  metallic  chromium  as  an  anode,  chromic  acid 
is  obtained.  In  the  former  case  the  process  is  spontaneous  and 
therefore  is  capable  of  doing  work.  Here  the  chromium  plays, 
in  all  respects,  the  part  of  a  base  metal,  simulating  zinc.  In  the 
second  case  work  must  be  expended  in  order  to  bring  the  chro- 
mium into  solution.  The  chromium  now  behaves  like  a  noble 
metal.  This  process  especially  directs  our  attention  to  the  fact 
that  the  electromotive  force  depends,  not  upon  the  substance,  but  upon  the 
process.  Moreover,  calculated  results  can  only  be  correct  when  the 
assumed  process  actually  takes  place  alone.  It  may  be  said  that  in 
the  first  case  the  velocity  of  the  formation  of  bivalent  chromium 
ions  is  very  great,  while  in  the  second  case  it  is  so  small  that  the 
formation  of  hexavalent  ions  takes  place.  Here  is  an  example  of  a 
real  transmutation,  i.e.  a  transformation  of  a  base  metal  into  a  noble 
one,  although  of  a  different  kind  from  that  sought  by  the  alchemists. 
At  present  nothing  further  is  known  of  the  conditions  upon  which 
this  change  in  reaction  velocity  depends. 

Analogous  relations  exist,  according  to  Luther,3  in  the  case  of 
ozone.  Ozone  possesses  different  electromotive  activity  and  enters  a 
reaction  with  different  valences  according  to  the  nature  of  the  indif- 
ferent electrode.  At  a  polished  platinum  anode  it  is  univalent, 
while  at  a  polished  iridium  anode  it  is  divalent. 

Furthermore,  in  the  case  of  metals  such  changes  in  valence  often 
take  place  with  changes  in  the  anodic  treatment.  For  example,  zinc 
and  copper,  as  anodes,  dissolve  at  least  partly  in  the  univalent  state 
in  the  presence  of  oxidizing  agents.  Since  these  univalent  ions  are 
strong  reducing  agents,  the  oxidizing  agent  is  reduced  or  hydrogen  is 
evolved  at  the  anode.  Thus  we  have,  as  a  noteworthy  result,  a 
reducing  action  at  the  anode.4 

1  Ztschr.  Elektrochem.,  9,  11  (1903).       *  Ztschr.  phys.  Chem.,  25,  729  (1898). 

*  Ztschr.  Elektrochem.,  11,  832  (1905). 

*  Luther  and  Schilow,  Ztschr.  phys.  Chem.,  46,  777  (1903). 


ELECTROMOTIVE  FORCE  279 

It  does  not  seem  impossible  that  the  latter  change  in  valence  may 
be  explained  in  a  manner  similar  to  that  given  on  page  267  for  the 
formation  of  complex  compounds  when  a  metal  is  dissolved.  In 
both  cases  there  may  be  a  continual  removal  of  one  kind  of  ions 
and  thus  a  tendency  to  favor  the  formation  of  this  kind  of,  ions. 
However,  a  definite  statement  of  the  cause  of  the  phenemenon  can- 
not be  given  until  the  subject  is  further  investigated. 

In  closing  this  discussion  of  passivity,  a  number  of  cases  in  which 
a  catalytic  influence  on  an  electro-chemical  process  has  been  observed 
will  be  presented. 

From  the  cell, 

Zn  -  ZnS04  solution  -HNOS  solution  -  Pt, 

an  electromotive  force  of  0.7  of  a  volt  according  to  the  investigation 
of  Ihle l  is  obtained  if  the  nitric  acid  solution  is  dilute  and  free  from 
nitrous  acid.  During  the  action  of  the  cell,  hydrogen  is  evolved  at 
the  platinum  electrode.  If  now  a  small  quantity  of  nitrous  acid 
be  added  near  the  platinum,  the  evolution  of  hydrogen  ceases  and 
simultaneously  the  electromotive  force  rises  to  about  one  volt. 

The  explanation  is  as  follows:  The  nitric  acid  is  an  oxidizing 
agent,  i.e.  it  is  capable  of  producing  hydroxyl  ions  by  undergoing 
decomposition  into  the  lower  oxides  of  nitrogen.  The  velocity  of 
the  formation  of  these  ions  is,  however,  under  ordinary  circum- 
stances practically  equal  to  zero.  Hence  the  nitric  acid  does  not 
"behave  like  an  oxidizing  agent,  but  like  any  other  acid,  and  therefore 
causes  hydrogen  to  be  evolved  at  the  cathode  as  usual.  The  nitrous 
acid  accelerates  the  formation  of  the  hydroxyl  ions,  and  since  this 
process  takes  place  spontaneously  with  a  much  higher  electromotive 
force,  it  replaces  the  evolution  of  hydrogen.  Consequently  the  elec- 
tromotive force  of  the  cell  rises. 

Finally,  the  observations  of  Forster 2  and  Voege 3  on  the  reduction 
of  potassium  chlorate  should  be  mentioned  in  connection  with  this 
subject.  The  former  found  that  when  high-current  densities  are 
used,  this  salt  is  scarcely  at  all  reduced  when  the  cathode  is  of 
platinum,  lead,  zinc,  or  nickel,  very  strongly  reduced  when  the  elec- 
trodes are  of  wrought  iron,  and  only  moderately  when  the  electrodes 
are  of  cobalt.  The  latter  investigator  found  that  in  acid  solutions 
the  activity  of  the  reduction  is  dependent  upon  the  material  used  foi 
the  cathode. 

1  Ztschr.  phys.  Chem.,  19,  577  (1896). 
2Ztschr.  Elektrochem.,  4,  386  (1897). 
8  J  Phys.  Chem.,  3,  577  (1899). 


280  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

It  is  very  remarkable  that,  according  to  the  choice  of  cathode 
metal,  reducing  action  can  be  made  to  take  place  to  different  stages 
of  the  same  depolarizer.  Thus  with  the  use  of  mercury  as  an  elec- 
trode, Tafel1  was  able  to  reduce  nitric  acid  quantitatively  to  hydroxyl- 
amine,  while  with  a  copper  electrode  covered  with  spongy  copper 
he  was  able  to  reduce  it  almost  quantitatively  to  ammonia.  If  blank 
copper  electrodes  are  used,  a  yield  06  about  15  per  cent  of  hydroxyl- 
amine  may  be  obtained.  It  is  evident  that  observations  such  as 
these  may  become  of  commercial  importance.  They  will  be  referred 
to  again  at  the  end  of  the  chapter  on  electrolysis  and  polarization. 

The  influence  of  the  anode  material  on  the  course  of  electrolytic 
oxidation  processes  is  shown  in  the  use  of  platinum  and  lead  perox- 
ide as  anodes  in  the  electrolytic  regeneration  of  chromic  acid.  Only 
when  the  latter  is  used  is  a  satisfactory  yield  obtained.  The  same 
difference  has  been  observed  in  the  oxidation  of  hydriodic  to  perhy- 
driodic  acid.  According  to  E.  Mtiller  and  Soller2  both  of  these 
cases  are  examples  of  the  catalytic  effect  of  the  cathode  material. 

Although  apparently  they  do  not  belong  to  this  discussion,  a  few 
observations  of  Luther3  will  be  mentioned.  He  found  that  the 
addition  of  a  small  quantity  of  a  dissolved  substance  which  exists 
in  several  different  states  of  oxidation  to  the  oxidizing  or  reducing 
agent  being  investigated,  is  without  influence  upon  the  potential- 
difference,  but  facilitates  its  measurement.  Thus  with  the  use  of 
platinum  electrodes  it  is  difficult  to  measure  the  potential-difference 
of  a  chromi-chromate  solution,  evidently  because  of  the  slowness  of 
the  reaction,  — 

Cr04'f  +  8  H'+  3  Q  (-):£<>•••  +  4  H20. 

By  the  addition  of  a  small  quantity  of  an  iron  salt,  this  difficulty 
is  removed.    The  concentration  ratio  ^-^  becomes  so  adjusted  that 

the  corresponding  potential-difference  is  equal  to  that  of  the  chromi- 
chromate  solution.     Now  since  the  velocity  of  the  reaction 


is    comparatively  great,  the   platinum  electrode  has  become  to  a 

greater  extent  unpolarizable.    Naturally  by  means  of  such  an  addition 

it  is  not  possible  to  obtain  a  continuous  large  current  of  electricity. 

From  these  examples,  which  might  easily  be  increased,  it  is  suffi- 

*Ztschr.anorg.  Chem.,  31,  289  (1902). 
*Ztschr.  Elektrochemie,  11,  863  (1905). 
*Ztschr.phys.  Chem.,  36,  400  (1901). 


ELECTROMOTIVE  FORCE  281 

ciently  evident  that  catalytic  influences  which  are  apparently  insig- 
nificant produce  very  considerable  effects  in  electro-chemistry.  It  is 
probable  that  in  the  future  very  remarkable  discoveries  may  be  made 
in  this  little-investigated  field. 

GENERAL  THEORY  OF  THE  COURSE  OF  THE  ELECTRO- 
CHEMICAL REACTIONS 

The  idea  that  possibly  the  process  of  evaporation  may  be 
explained  by  the  formation  of  a  layer  of  saturated  vapor  directly  on 
the  surface  of  the  liquid  which  gradually  diffuses  into  the  surround- 
ings, and  that  the  rate  of  evaporation  depends  on  the  rate  of  this 
diffusion,  was  first  presented  by  Stefan.1  Somewhat  later,  and 
apparently  without  knowledge  of  Stefan's  work,  Noyes  and  Whit- 
ney2 came  to  an  analogous  conclusion  in  studying  the  velocity  of 
solution  of  solid  bodies.  They  found  that  the  latter  is  proportional 
to  the  difference  in  concentration  of  the  saturated  solution  and  that 
of  the  solution  surrounding  the  body  at  the  time  the  velocity  of 
solution  was  measured. 

The  theory  put  forward  for  these  two  special  cases  was  generalized 
by  Nernst,3  and  in  this  form  it  was  endeavored  to  apply  it  to  all 
chemical  reactions  taking  place  in  heterogeneous  systems.  Accord- 
ing to  the  expanded  theory,  equilibrium  always  exists  at  the  boundary 
surface  of  two  reacting  phases,  so  that  the  reaction  velocity  is  deter- 
mined solely  by  the  rate  of  decrease  of  the  difference  between  the 
concentration  at  the  surface  and  that  in  the  interior  of  the  phase. 
If  now  more  comprehensible  relations  be  obtained  by  reducing  the 
thickness  of  the  layer  in  which  the  fall  in  concentration  takes  place 
to  a  certain  value  I  by  suitable  stirring  of  the  solution,  then  the 
velocity  of  reaction  is  represented  by  the  equation, 


i 

where  DCO  represents  the  diffusion  coefficient,  s  the  contact  surface  of 
the  reacting  phases,  and  C  —  C'  the  concentration-difference  involved. 
The  value  of  I  is  dependent  on  the  temperature,  the  solvent,  and  the 
speed  of  stirring. 

From  this  theory  a  number  of  interesting  conclusions  may  be 

1  Wied.  Ann.,  41,  725  (1890). 

2  Ztschr.  phys.  Chem.,  23,  689  (1897). 

8  Ztschr.  phys.  Chem.,  47,  62  ;  and  also  Brunner,  Ztschr.  phys.  Chem.,  47,  66 
(1904). 


282  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

drawn.  The  velocity  of  solution  of  a  rod  of  benzoic  acid  in  pure 
water  would  be  for  a  given  surface,  temperature,  and  speed  of  stir- 
ring, proportional  to  the  product  of  the  coefficient  of  diffusion  and  the 
concentration  of  the  saturated  solution,  i.e. 

U.  =  const,  x  DCO  x  C. 

In  this  case  C'  is  equal  to  zero.  If  now  at  the  same  temperature 
and  the  same  speed  of  stirring,  a  rod  of  any  difficultly  soluble  oxide 
or  hydroxide,  with  a  surface  equal  to  that  of  the  rod  of  benzoic  acid, 
be  placed  in  a  saturated  solution  of  benzoic  acid,  then  its  rate  of 
solution  will  be  equal  to  that  of  the  rod  of  benzoic  acid  in  pure 
water,  i.e.  equal  to  a  const,  x  DCO  x  C.  This  must  be  so,  for  there  is 
always  at  the  surface  of  the  solid  oxide  a  layer  of  liquid  saturated 
with  it,  i.e.  a  layer  of  a  solution  of  hydrogen  ions  of  a  very  small 
concentration  corresponding  to  the  slight  solubility  of  the  oxide. 
The  benzoic  acid  which  diffuses  to  the  surface  of  the  oxide  is  com- 
pletely neutralized ;  its  concentration  is  thus  reduced  practically  to 
zero.  Hence  the  rate  of  solution  of  the  oxide  is  governed  by  the 
coefficient  of  diffusion  of  the  benzoic  acid  D^  and  the  concentration 
of  the  saturated  solution  C  (not  considering  the  constant  involved). 

Plainly  nothing  essential  is  changed  if  a  large  rod  of  some  base 
metal  such  as  magnesium  be  substituted  for  the  rod  of  oxide.  Since 
the  concentration  of  hydrogen  ions  at  the  surface  of  the  metal  is  very 
small,  it  may  be  considered  to  be  practically  equal  to  zero.  The  rate 
of  solution  of  the  metal  would  then  depend  only  on  the  velocity  of 
diffusion  of  acid  to  its  surface  where  hydrogen  ions  lose  their 
charges,  magnesium  ions  form,  and  hydrogen  gas  is  evolved.  As 
above  indicated,  this  is  true  provided  all  processes  which  consist 
in  the  simple  giving  up  or  taking  on  of  electrical  charges  by  a  sub- 
stance at  the  boundary  surface  between  metallic  and  electrolytic  con- 
ductors are  like  those  which  consist  in  mere  transition  through  a 
boundary  surface  without  electrical  change,  taking  place  so  rapidly 
that  equilibrium  is  constantly  maintained  at  the  boundary  surface. 
It  makes  no  difference  here  whether  or  not  the  substance  goes  over 
into  another  phase,  i.e.  electrolytic  separation  and  solution,  or 
whether  or  not  one  of  the  substances  dissolved  in  the  electrolyte  is 
transformed  into  another  soluble  substance,  i.e.  real  electrolytic 
oxidation  and  reduction. 

We  may  proceed  a  step  farther.  If  the  rod  used  in  the  above- 
cited  case  be  replaced  (other  conditions  remaining  the  same)  by  any 
unattacked  electrode  of  the  same  form  and  size,  and  if  a  cathode 
potential  be  imparted  to  it  such  that  the  concentration  of  H  ions 


ELECTROMOTIVE  FORCE  283 

formed  directly  at  its  surface  is  very  small,  then  the  electric  current 
(which  can  pass  only  through  the  discharging  of  H  ions)  is  equiv- 
alent to  the  quantity  of  H  ions  furnished  by  the  diffusion  of  the 
acid  and  the  electrolytic  transference.  The  transference  of  H  ions 
can  be  eliminated  by  taking  a  solution  containing  a  sufficient  excess 
of  salt.  The  velocity  of  reaction,  that  is,  the  current-strength,  must 
then  be  equal  to  the  velocity  of  solution  of  the  oxide  rod  in  the  same 
acid  solution.  Hence  after  a  certain  cathode  potential  is  reached, 
the  current-strength  remains  constant  and  independent  of  a  further 
increase  of  this  potential.  This  holds  only  within  certain  limits,  i.e. 
until  some  other  process  begins  also  to  take  place. 

Experimental  results  which  have  been  obtained  are  in  good  agree- 
ment with  this  theory. 

In  the  case  of  all  electrolytic  reductions  and  oxidations  for  which 
the  assumption  holds  that  all  reactions  coming  into  consideration 
are  very  rapid  as  compared  with  the  velocity  of  diffusion,  the 
velocity  of  diffusion  and  the  kind  of  stirring  are  the  chief  factors 
influencing  the  processes  at  the  electrodes. 

There  are  also  processes  which  take  place  at  the  electrodes  which 
not  only  consist  in  the  giving  up  or  taking  on  of  electric  charges,  but 
also  are  accompanied  by  pure  chemical  reactions  (in  a  homogeneous 
system).  Such  a  reaction  is  the  following :  — 

Chinone  ^±  Hydrochinone.1 

According  to  the  discussion  on  page  267,  we  must  consider  that 
this  reaction  results  from  the  discharging  of  hydrogen  or  hydroxyl 
ions  at  the  electrode,  and  the  reacting  of  the  gas  so  formed  with  the 
chinone  or  the  hydrochinone,  as  the  case  may  be.  The  latter  pure 
chemical  reaction,  however,  proceeds  very  slowly.  In  such  cases 
the  velocity  of  reduction  of  chinone  or  the  velocity  of  oxidation  of 
hydrochinone  is  independent  of  the  more  rapid  process  of  diffusion 
and  is  characteristic  of  the  process  in  question.  It  is  dependent  on 
the  character  of  the  depolarizer.  Such  slow  reactions  as  the  oxida- 
tion or  reduction  reaction  just  mentioned  are  often  met  with  in  the 
case  of  organic  substances.  With  such  depolarizers  hydrogen  or 
oxygen  is  evolved  at  the  electrode  at  a  less  current  density  than  it 
is,  under  otherwise  the  same  conditions,  in  the  case  of  very  active 
depolarizers. 

Even  in  these  latter  reactions,  it  should  particularly  be  noted  that 
it  has  been  assumed  that  the  transference  of  substances  or  electrical 

1  Haber  and  Russ,  Ztschr.  phys.  Chem.,  47,  257  (1904). 


284  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

charges  from  one  phase  to  another  takes  place  with  infinite  rapidity. 
The  fundamental  assumption  of  Nernst  therefore  still  remains. 
Whether  or  not  this  assumption  is  untenable  in  many  cases  is  still 
an  open  question.  As  far  as  the  process  of  electrical  charging  or 
discharging  is  concerned,  it  is  probably  always  rapid,  for  in 
homogeneous  systems  reactions  between  ions  are  generally  (always  ?) 
very  rapid.  Nevertheless  we  know  of  no  reason  at  present  why  of 
necessity  it  must  be  rapid.  There  is  still  less  reason  for  thinking 
that  other  processes  taking  place  between  phases  are  generally  (or 
always)  rapid.  It  is  known  that  reactions  in  homogeneous  systems 
often  take  place  slowly,  and  no  reason  is  apparent  why  reactions  in 
heterogeneous  systems  may  not  also  take  place  slowly. 

It  is  evident  that  these  questions  are  most  intimately  related  to 
the  phenomenon  of  passivity  (see  page  275).  The  assumption  of  a 
lack  of  a  velocity  of  ionization  made  in  considering  passivity  does 
not  necessarily  contradict  the  fundamental  assumption  of  Nernst. 
It  is  quite  possible  that  the  transition  from  the  metallic  to  the 
ionic  state  may  consist,  not  only  of  the  taking  on  of  an  electrical 
charge,  but  also  of  a  number  of  other  processes,  any  one  of  which 
by  taking  place  slowly  may  cause  the  appearance  of  the  phenomenon 
of  passivity.  This  latter  case  is  very  similar  to  that  of  the  reaction, 

Chinone  "^  Hydrochinone. 
A  further  explanation  must  be  left  to  the  future. 

ELEMENTS  POSSESSING  DOUBLE  NATURES 

Although  up  to  the  present  we  have  always  spoken  of  substances, 
like  the  metals,  which  can  furnish  only  positive  ions,  or  of  substances, 
like  oxygen,  which  can  furnish  only  negative  ions,  it  is  not  unreason- 
able to  question  whether  or  not  a  single  substance  may  possess  the 
power  of  forming  both  negative  and  positive  ions.  In  the  year 
1900  I  stated  the  following  in  the  second  edition  of  this  book. 
"  There  are  many  indications  that  such  cases  exist.  Thus  if  a  solu- 
tion of  selenous  or  selenic  acid  be  electrolyzed,  a  deposition  of 
metallic  selenium  is  obtained  at  the  cathode.  This  indicates  the 
existence  of  positively  charged  selenium  ions.  On  the  other  hand, 
a  study  of  hydrogen  selenide  or  sodium  selenide  leads  to  the  con- 
clusion that  selenium  also  forms  negative  ions.  The  behavior  of 
sulfur  and  of  tellurium  is  similar  to  that  of  selenium,  and  even  in 
the  case  of  the  halogens,  it  is  not  entirely  certain  that  under  all 
circumstances  they  form  negative  ions."  In  the  meantime  Walden 


ELECTROMOTIVE  FORCE  285 

i 

has  carried  out  conductivity  measurements  in  solvents  other  than 
water  which  substantiate  this  view.  He1  found  that  the  conduc- 
tivity of  liquid  sulfur  dioxide  is  considerably  increased  when 
bromine  is  dissolved  in  it,  and  that  of  sulfuryl  chloride  is  also 
increased  by  the  addition  of  iodine.  If  now  we  maintain  that  the 
electrical  conductance  of  solutions  is  due  to  the  presence  of  ions, 
then  we  come  to  the  conclusion  that  the  bromine  and  iodine  in  these 
two  solutions  dissociates  according  to  the  equations,  — 


and  I2^±r  +  r. 

Closely  related  to  the  question  of  the  possibility  of  an  element 
existing  in  solution  both  in  the  form  of  positive  and  of  negative 
ions  is  that  of  the  possibility  of  one  and  the  same  element 
going  into  solution  by  being  electromotively  active  both  as  an  anode 
and  as  a  cathode.  As  a  matter  of  fact,  this  remarkable  behavior  is 
exhibited  by  tellurium  when  used  in  a  completely  symmetrical  arrange- 
ment 2  in  an  alkali  solution.  At  the  anode  it  goes  into  solution  as 
Tez",  where  x  varies  between  1  and  2  according  to  the  conditions 
of  experiment,  and  at  the  cathode  as  Te""  which  unite  largely 
with  the  OH  ions  to  form  the  complex  ion  Te03".  This  explanation 
at  least  seems  the  simplest  one  offered  up  to  the  present  time.  Al- 
though investigations  of  other  elements  have  not  yet  been  concluded, 
they  appear  to  behave  in  a  similar  manner. 

It  is,  at  all  events,  of  great  interest  to  learn  that  there  is  no 
sudden  change  between  "positive"  and  "negative"  elements,  but 
rather  a  gradual  transition  through  a  number  of  elements  which 
may  be  either  positive  or  negative  according  to  circumstances,  i.e. 
through  elements  which  possess  double  natures. 

1  Ztschr.  phys.  Chem.,  43,  385  (1903). 

2  M.  Le  Blanc,  Ztschr.  Elektrochem.,  11,  813  (1905)  ;  and  12  (Spring  of  1906). 


CHAPTER   VIII 

ELECTROLYSIS  AND  POLARIZATION 

THE  phenomena  observed  when  an  electric  current  is  conducted 
through  an  electrolyte  between  inactive  electrodes,  as  gold,  platinum, 
carbon,  etc.,  will  now  be  considered.  It  has  long  been  known  that 
the  current  produces  a  decomposition  of  the  electrolyte  at  the  elec- 
trodes, and  that  its  electromotive  force  is  thereby  reduced.  The 
two  facts  are  evidently  related.  The  performance  of  an  amount  of 
work,  more  or  less  considerable  according  to  circumstances,  is  neces- 
sary to  bring  about  the  decomposition  of  an  electrolyte  (as,  for 
example,  hydrochloric  acid  into  hydrogen  and  chlorine),  and  this 
work  is  done  by  the  electric  current.  When  such  reduction  of  the 
electromotive  force  occurs,  polarization  is  said  to  take  place.  The 
phenomenon  was  formerly  very  little  understood,  and  it  is  only 
within  the  last  few  decades  that  its  explanation  has  become  possible. 

If  a  current  flows  for  a  time  through  the  above-described  arrange- 
ment, and  is  then  interrupted,  the  two  electrodes  being  connected 
through  a  galvanometer,  it  will  be  observed  that  an  electric  current, 
which  rapidly  becomes  weaker,  passes  between  the  electrodes  in  a 
direction  opposite  to  that  of  the  first  or  applied  current.  This  is 
spoken  of  as  the  polarization  current,  and  its  electromotive  force  is 
called  the  electromotive  force  of  polarization.  From  the  following  it 
will  be  evident  that  this  current  is  derived  from  the  tendency  of  the 
materials  separated  in  the  neutral  condition  to  return  to  the  ionic 
condition. 

Ohm's  law,  applied  to  a  circuit  possessing  a  certain  primary 
electromotive  force  FI,  and  containing  a  "  polarization  cell,"  is  rep- 
resented by 


where  F2  is  the  electromotive  force  of  polarization,  c  the  current, 
and  B  the  total  resistance  of  the  circuit. 

Methods  of  measuring  Polarization.1  —  As  already  seen,  the  electro- 

1  For  further  particulars,  see  Ostwald-Luther,  Physiko-chemische  Messungen, 
p.  390. 

286 


ELECTROLYSIS  AND  POLARIZATION  287 

motive  force  of  polarization  is  not  a  constant,  but  rapidly  diminishes 
when  the  primary  electromotive  force  is  removed;  its  magnitude  is 
therefore  best  determined  during  the  passage  of  the  primary  current. 
The  accompanying  figure  represents  an  arrangement  which  may  be 
used  for  the  measurement.1 

One  circuit  is  represented  by  1,  2,  a,  1,  and  the  other  by  2,  e,  b,a,2; 
1  is  the  source  of  the  electricity,  2  the  polarization  cell,  e  a  compen- 
sation electrometer,  b  a  known  electromotive  force,  which  may  be 
altered  at  will,  and  a  a  tuning  fork  commutator  (or,  better,  a  double 
commutator  driven  by  a  motor),  which  vibrates  very  rapidly.  The 
arrangement  is  such  that  at  a  one  circuit  is  opened  and  the  other 
simultaneously  closed,  then  the  latter  opened  and  the  former  closed, 
etc.,  with  each  vibration  of  the  tuning  fork.  The  result  is  practically 
the  same  as  though  both  primary  and  polarization  current  were  inde- 
pendently active.  Thus  the  electromotive  force  of  the  latter  may  be 
measured  under  the  same  conditions  as  if  the  primary  circuit  were 
continually  closed.  It  is  only  necessary  to  alter  b  until  the  electrom- 
eter shows  a  condition  of  equilibrium ;  b  is  then  the  desired  value. 


FIG.  49 

As  the  electromotive  force  of  galvanic  elements  is  due  to  two  or 
more  potential-differences,  so  also  in  the  electromotive  force  of  po- 
larization two  single  potential-differences  are  found  located  at  the 
two  electrodes.  In  order  to  measure  them  separately,  the  method  of 
Fuchs  is  employed.  Its  arrangement  is  shown  in  Figure  50.  A 
double  U-tube  is  filled  with  the  solution  of  the  electrolyte  e  whose 
polarization  is  to  be  measured,  a  and  6  are  two  indifferent  electrodes 
connected  with  the  source  Q  of  the  primary  or  polarizing  current. 
If  the  potential-difference  at  b  is  to  be  measured,  the  bent  glass  tube 
of  the  normal  electrode  N  (page  246),  filled  with  normal  potassium 
chloride  solution,  is  inserted  at  c  in  the  electrolyte  e,  and  b  is  con- 
nected with  the  mercury  of  the  normal  electrode  by  means  of  the 
platinum  wire  of  the  latter.  An  element  thereby  results,  consisting 

1  Le  Blanc,  Ztschr.  phys.  Chem.,  5,  469  (1890). 


288 


A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 


of  two  electrodes  and  two  electrolytes,  and  the  electromotive  force 
of  the  combination  is  measured  by  the  usual  apparatus  at  M.  The 
potential-difference  between  b  and  e  may  then  be  determined  by  sub- 
traction of  the  normal  electrode  potential,  and  that  at  the  surface 
of  contact  between  the  liquids  from  the  total  electromotive  force. 
For  determining  the  potential-difference  between  a  and  e  the  process 
is  analogous,  and  using  a  primary  or  polarizing  current,  whose 
electromotive  force  gradually  increases  from  zero,  it  is  observed  that 
the  electromotive  force  of  polarization  is  at  first  very  nearly  equiva- 
lent to  that  of  the  primary  current.  As  the  latter  becomes  higher 
the  former  falls  gradually  away  from  it  in  magnitude,  nevertheless 
always  increasing  to  some  extent.  The  much-sought-after  maximum 
of  polarization  does  not  actually  exist. 


FIG.  50 

Decomposition  Values  of  the  Electromotive  Force.  The  Hydrogen- 
Oxygen  Cell.  Primary  and  Secondary  Decomposition  of  Water. — 

There  is  another  characteristic  point  for  the  different  electrolytes. 
A  continuous  current  flows  and  a  continuous  decomposition  only 
takes  place  when  the  electromotive  force  exceeds  a  certain  value. 
If  an  electromotive  force  less  than  the  above  be  impressed,  only  an 
instantaneous  passage  of  electricity  takes  place,  which  may  be  made 
evident  by  inserting  a  galvanometer  into  the  circuit.  The  needle  of 
the  galvanometer  is  at  first  deflected,  but  returns  very  nearly  to  its 
original  position  (the  effect  of  secondary  disturbing  influences  will 
be  considered  later).  This  does  not  happen  when  the  applied  elec- 
tromotive force  has  reached  the  value  in  question. 

A  better  view  of  these  relations  may  be  obtained  by  plotting  the 
current  on  the  ordinate  and  the  corresponding  electromotive  force  on 
the  abscissa  of  a  coordinate  system.  The  curves  thus  obtained  (see 
later,  Figure  51)  all  show  a  more  or  less  abrupt  turning  point  at 
which  the  curve  changes  its  direction.1 

1  As  has  already  been  indicated,  the  potential-fall  due  to  the  resistance  of  the 
electrolyte  must  either  be  avoided  or  taken  into  consideration  in  the  calculations. 


ELECTROLYSIS  AND   POLARIZATION  289 

Le  Blanc  determined  the  magnitudes  of  these  decomposition  values 
for  a  great  many  electrolytes,  chiefly  in  normal  solutions.  They 
may  be  very  exactly  determined  for  salts  from  which  a  metal  is  pre- 
cipitated by  the  current,  but  for  other  salts,  as  well  as  for  acids  and 
alkalies,  they  are  less  easily  found.  The  following  decomposition 
values  were  found  for  salts  from  which  the  metal  is  deposited.1 

ZnS04      =  2.35  volts  Cd(N03)2  =  1.98  volts 

ZnBr2       =1.80  volts  CdS04       =  2.03  volts 

NiS04      =2.09  volts  CdCl2        =  1.88  volts 
NiCl2       =  1.85  volts 

Pb(N03)2  =  1.52  volts  CoS04       =  1.92  volts 

AgN03     =  0.70  volt  CoCl2         =  1.78  volts 

The  decomposition  values  for  sulfates  and  nitrates  of  the  same 
metal,  as  shown  by  the  experiments  with  cadmium  salts  and  other 
experiments  with  the  alkalies,  are  nearly  equal.  As  is  evident,  the 
values  for  the  various  metals  are  different.  The  conclusion  to  be 
drawn  from  the  corresponding  values  for  the  acids  and  bases  is  that 
there  exists  a  maximum  decomposition  point,  which  is  exhibited 
by  most  of  the  compounds  and  exceeded  by  none.  This  is  about 
1.67  volts.  Among  the  acids,  however,  several  gave  values  below 
this  maximum.  The  following  tables  contain  the  values  for  acids 
and  bases :  — 

Acids 

Sulfuric       .        .        ...        .        .        .  =  1.67  volts 

Nitric =  1.69  volts 

Phosphoric          .        .        .         .        .        .  =  1.70  volts 

Monochloracetic          .        .        *        .         .  =  1.72  volts 
Dichloracetic       .        .        V       .       V       •  :      =  1.66  volts 

Malonic    '\      r  ..."      *        .     •  V        .  =  1.69  volts 

Perchloric  .     /.     :    .        .        .        *  =  1.65  volts 

Dextrotartaric     .     ~   .        «        •        «        .  =  1.62  volts 

Pyrotartaric        .        i     -   •        •        •        •  =  1.57  volts 

Trichloracetic      .        .        .        .        .        .  =  1.51  volts 

Hydrochloric       .         ...•.»••-«•        .         .  =  1.31  volts 

Hydrazoic  .         »«.         .         .  =  1.29  volts 

Oxalic         .         .....        .        .  =0.95  volt 

Hydrobromic =  0.94  volt 

Hydriodic =  0.52  volt 

1  Ztschr.phys.  Chem.,  8,  299  (1891). 


290  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 


Sodium  hydrate  .        .         .        .  =1.69  volts 

Potassium  hydrate =1.67  volts 

Ammonium  hydrate    .         .         .         .        *  .  =  1.74  volts 

^  n.  Methylamine        .        .         .  ...  =  1.75  volts 

-J- n.  Diethylamine       .   •    ,. /     .         .        .  =  1.68  volts 

^  n.  Tetramethyl  ammonium  hydrate          .  =  1.74  volts 

The  alkali  and  alkali  earth  salts  of  the  highly  dissociated  acids 
with  maximum  decomposition  values,  as  sulfates  and  nitrates,  have 
nearly  the  same  decomposition  point,  i.e.  about  2.20  volts.  The 
chlorides,  bromides,  and  iodides  have  lower  values,  independent  of 
the  nature  of  the  alkali  metal.  Additivity  is  exhibited,  owing  to  the 
mutual  independence  of  the  potential-differences  produced  at  the  two 
electrodes.  Differences  between  the  values  for  the  various  halogen 
compounds  of  the  alkalies,  hydrogen,  and  the  metals  are  nearly 
equal ;  for  example,  the  difference  between  hydrochloric  and  hydro- 
bromic  acid  is  the  same  as  that  between  sodium  chloride  and 
sodium  bromide. 

The  salt  of  a  slightly  dissociated  acid,  as  sodium  acetate,  or  of  a 
slightly  dissociated  base,  as  ammonium  sulfate,  always  exhibits  a 
lower  value  than  that  of  a  highly  dissociated  acid  or  base,  providing 
the  acid  and  base  possess  the  maximum  decomposition  value.  The 
halogen  salts  of  ammonium  have  lower  decomposition  values  than  the 
corresponding  salts  of  the  alkalies ;  and,  in  fact,  the  differences 
between  corresponding  salts  are  equal. 

Concerning  the  effect  of  dilution  in  the  case  of  bases  and  acids 
which  on  electrical  decomposition  evolved  oxygen  and  hydrogen  at 
the  electrode,  the  decomposition  values  are  independent  of  the 
dilution,  and  this  is  true  for  all  the  acids  excepting  those  whose  de- 
composition values  are  below  the  maximum.  For  these,  the  value 
rises  with  increasing  dilution,  and  finally  reaches  the  maximum. 
This  is  very  marked  in  the  case  of  hydrochloric  acid. 


CONCENTRATION 

DECOMPOSITION  POINT 

f  Normal  hydrochloric  acid 
$  Normal  hydrochloric  acid 
£  Normal  hydrochloric  acid 
^  Normal  hydrochloric  acid 
3*3  Normal  hydrochloric  acid 

1.26  volts 
1.34  volts 
1.41  volts 
1.62  volts 
1.69  volts 

ELECTROLYSIS  AND  POLARIZATION  291 

It  is  also  worthy  of  note  that  when  the  maximum  value  is  reached, 
the  acid  solution  is  no  longer  decomposed  into  chlorine  and  hydrogen, 
but  into  hydrogen  and  oxygen. 

The  above  experiments  were  carried  out  with  platinum  electrodes. 
If  other  electrodes  be  used,  as  gold  or  carbon,  different  numerical  values 
are  obtained,  but  the  general  relations  between  them  remain  unaltered. 

In  order  to  obtain  a  better  insight  into  polarization  phenomena 
Le  Blanc1  investigated  the  potential-difference  at  the  electrode 
where  the  metal  is  electrolytically  deposited  (the  cathode),  when  the 
electromotive  force  of  the  primary  current  is  gradually  increased 
from  zero.  He  found  that  the  potential-difference  at  the  decomposi- 
tion point  is  equal  to  that  which  the  precipitating  metal  would  itself 
exhibit  in  the  solution.  For  example,  a  normal  solution  of  cadmium 
sulfate  was  decomposed  at  a  primary  electromotive  force  of  2.03 
volts.  The  potential-difference  of  the  electrode  where  the  cadmium 
separated  was,  — 

3-e   electrode  -  electrolyte  ==          "»7«. 

Metallic  cadmium  placed  in  the  solution  also  gave  —  0.72  volt.  In 
many  solutions  the  electrode  exhibited  the  potential-difference  due 
to  the  separating  metal  before  the  decomposition  point  of  the  solu- 
tion is  reached.  For  instance,  in  silver  nitrate  the  electrode  had 
the  value  of  pure  silver  in  silver  nitrate  even  below  the  decomposi- 
tion point  (0.70).  This  is  due  to  the  great  tendency  of  the  silver 
ions  to  separate  as  electrically  neutral  metal. 

It  was  also  possible  to  demonstrate  that  the  material  of  the  indif- 
ferent electrodes,  providing  no  alloy  is  formed,2  is  without  influence 
upon  the  magnitude  of  these  potential-differences.  The  results  were 
the  same  whether  gold,  platinum,  carbon,  or  any  other  metal  more 
positive  than  that  in  solution  was  used.  From  this  it  is  evident  that 
the  electrode  itself  possesses  no  "  specific  attraction "  for  the  elec- 
tricity, as  formerly  was  imagined. 

The  process  of  precipitation  and  solution  of  the  metals  is,  there- 
fore, to  be  considered  as  reversible.  It  may  be  represented  as  fol- 
lows :  If  an  indifferent  electrode  be  placed  in  the  solution  of  a  salt  of 
a  metal,  a  very  small  quantity  of  the  ions  leave  the  ionized  state  and 
deposit  upon  the  electrode  in  the  metallic  form.  This  process  goes 
on  until  the  tendency  of  the  ions  to  deposit  in  the  metallic  state  is 
exactly  compensated  by  the  electrostatic  attraction  which  exists  be- 
tween the  positively  charged  electrode  and  the  negatively  charged 

1  Ztschr.phys.  Chem.,  12,  333  (1893). 

1  For  further  particulars,  see  Coehn  and  Dannenberg,  Ztschr.  phys.  Chem.,  38, 
609,  1901. 


292  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

solution.  The  quantity  of  ions  deposited  is,  therefore,  dependent 
upon  the  tendency  of  the  ions  to  persist  in  the  ionized  state.  Up 
to  the  present  we  have  always  spoken  of  the  tendency  of  the  metal 
to  pass  into  the  ionized  state.  Now  we  will  speak,  as  naturally  we 
may  with  equal  right,  of  the  tendency  of  the  ions  to  remain  as  such. 
To  express  this  exertion  of  the  ions  to  hold  their  electrical  charges, 
the  expression  holding  power  (Haftintensitat)  is  often  used.  Nu- 
merically this  holding  power  is  equal  to  the  electromotive  force 
which  is  required  to  deposit  an  ion  in  the  neutral  state. 

A  certain  potential-difference  must,  therefore,  exist  at  the  elec- 
trode, there  being  some  metal  upon  it  and  the  corresponding  ions  in 
the  solution.  The  magnitude  of  this  potential-difference  need  not 
be,  and  almost  never  is,  the  same  as  found  when  the  massive  metal 
is  in  contact  with  the  solution,  for  the  metal  deposited  upon  the  elec- 
trode does  not  reach  the  concentration  of  the  massive  metal.  The 
conclusion  seems  strange  at  first,  for  it  is  customary  to  consider  the 
concentration  of  a  metal  as  unalterable.  This  is  only  the  case  above 
a  definite  limit.  If  the  metal  is  not  present,  at  least  to  the  extent 
of  a  molecular  layer,  it  does  not  act  as  the  massive  metal.  This  has 
been  shown  by  Oberbeck1  and  Kb'nigsberger  and  Miiller.2  When 
the  metal  of  a  salt  solution  was  precipitated  upon  a  platinum  plate, 
the  latter  exhibited  in  the  corresponding  metal  solutions  the  poten- 
tial-difference characteristic  of  the  massive  metal  as  soon  as  a  certain 
amount  had  been  deposited.  Below  this  point  the  electrode  ex- 
hibited smaller  potential-differences  corresponding  to  the  lower  con- 
centrations of  the  metal.  This  fact  need  not  be  surprising  when  it 
is  recalled  that  gases  and  dissolved  substances  have  solution  pres- 
sures dependent  upon  their  concentration. 

If  the  source  of  an  electromotive  force  be  connected  with  the 
electrode  in  such  a  manner  as  to  tend  to  separate  a  metal  from  the 
solution,  it  works  against  the  electrostatic  attraction,  and  more  ions 
can  separate  as  metal.  The  concentration  of  the  metal  upon  the 
electrode  is  thereby  increased,  and  consequently  also  its  solution 
pressure  p,  which  tends  to  prevent  a  further  deposition  of  the 
metal,  and  soon  entirely  prevents  it.  To  deposit  more  metal  it  is 
necessary  to  impress  a  still  greater  potential-difference.  This  con- 
tinues until  the  maximum  concentration  of  the  metal  is  reached  — 
that  is,  until  the  electrode  acts  as  the  massive  metal.  A  continual 
deposition  may  then  take  place  without  further  increase  of  the  ap- 
plied electromotive  force,  providing,  naturally,  that  the  osmotic  pres- 

1  Wied.  Ann.,  31,  336  (1887). 

2  Phys.  Ztschr.,  6,  847  and  849  (1905). 


ELECTROLYSIS  AND  POLARIZATION  293 

sure  of  the  ions  P  remain  unaltered.  When  strong  currents  are 
used  P  does  not  remain  constant,  but  gradually  diminishes,  and  con- 
sequently the  potential-difference  at  the  electrode  increases. 

It  must  be  observed  that  the  separation  of  positive  ions  at  one 
electrode  as  neutral  substance  is  necessarily  accompanied  by  the 
simultaneous  deposition  of  the  corresponding  amount  of  negative 
ions  at  the  other.  Considerations  analogous  to  the  above  evidently 
apply  to  the  negative  electrode.  If,  for  example,  oxygen  is  set  free, 
the  concentration  of  the  gas  gradually  increases;  and,  when  the 
solution  is  saturated,  has  its  greatest  value,  and  consequently  also 
its  maximum  solution  pressure  (which  opposes  the  further  decom- 
position of  the  electrolyte).  If  more  separates,  it  escapes  into  the 
air.  It  will  now  be  understood  why  a  certain  electromotive  force 
is  necessary  to  induce  continuous  decomposition  in  an  electrolyte ; 
this  only  occurs  when  the  concentrations  of  the  two  substances 
separating  at  the  electrodes  have  reached  their  maximum  values. 
It  is  also  evident  that  the  electrodes  upon  which  metals  are  de- 
posited should  exhibit  the  potential  characteristic  of  the  massive 
metal  when  the  decomposition  point  is  reached.  But  it  is  evi- 
dently unnecessary  that  these  maxima  of  concentration  for  both 
electrodes  should  be  reached  simultaneously;  it  may  sometimes  be 
reached  at  an  electrode  before  the  decomposition  point  of  the  solu- 
tion can  be  attained,  as  is  the  case  with  a  silver  solution.  The 
decomposition  point  of  normal  silver  nitrate  is  0.70  volt,  but  the 
potential-difference  at  the  electrode  upon  which  silver  is  deposited 
is  of  the  same  magnitude  as  that  between  massive  silver  and  the 
solution  long  before  this  decomposition  value  is  reached. 

The  polarization  due  to  metal  ions  having  been  considered,  atten- 
tion will  now  be  directed  to  the  phenomena  presented  when  gaseous 
or  dissolved  substances  are  separated.  These  are  somewhat  more 
complicated,  and  have  greatly  increased  the  difficulty  of  understand- 
ing the  process  of  polarization.  As  a  simple  case,  the  following  cell 
will  be  considered  :  — 

Pt  (platinized)  in  hydrogen  —  water  (with  a  dis- 
solved electrolyte,  such  as  H2S04) , 

Pt  (platinized)  in  oxygen \ 

Consider  the  two  gases  to  be  under  atmospheric  pressure. 

The  cell  at  17°  has  an  electromotive  force  of  about  one  volt,  and 
is,  as  was  first  shown  by  Le  Blanc,  to  be  considered  reversible  for 
small  current  densities.  If  an  equal  opposing  electromotive  force 
be  connected  with  this  cell,  a  condition  of  equilibrium  exists ;  when 


294  A   TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

a  lower  electromotive  force  is  applied,  water  is  produced  by  the 
oxygen  and  hydrogen  of  the  cell,  and  when  the  electromotive  force 
of  the  opposing  current  is  greater,  water  is  decomposed.  Smale1 
calculated  the  temperature  coefficient  of  this  cell  from  the  Helin- 
holtz  formula,  using  the  known  heat  of  formation  of  water  under 
constant  pressure  (67,534  cal.  at  17°)  and  the  measured  electro- 
motive force  as  data  :  — 


96540  x  1.07  -  33767  x  4.189  =  §T— ; 

38152      _  dF 
~96540x290~dT; 

J|  =  -0.00136. 

Q  is  v"^*,  since  the  heat  effect  corresponding  to  one  equivalent  of 

the  substance  is  employed.  Experimental  determinations  gave  as  a 
mean  value  between  0°  and  68°,  0.00141,  and  between  0°  and  100°, 
0.00143  (obtained  later  by  L.  Glaser),  which  is  a  satisfactory  agree- 
ment with  the  calculated  value. 

It  has  recently  been  shown2  that  the  electromotive  force  of  the 
hydrogen-oxygen  cell  at  atmospheric  pressure  and  room  temperature 
must  be  1.22  volts,  a  value  which  is  considerably  higher  than  that 
obtained  by  earlier  investigators,  who,  perhaps  because  of  the  forma- 
tion of  oxides,  never  succeeded  in  completely  saturating  the  oxygen 
electrode.  The  highest  value  which  has  been  found  is  1.14  volts. 
This  change  in  the  value  of  the  electromotive  force  of  the  cell 
has,  however,  no  influence  upon  the  above  calculation,  because  the 
cell  is  capable  of  producing  work  reversibly,  whatever  the  pres- 
sures of  the  gases. 

Furthermore,  at  high  temperatures,  the  agreement  between  the 
value  of  the  electromotive  force  calculated  from  thermodynamical 
considerations  and  that  found  experimentally  is  very  satisfactory.3 

It  may  now  be  predicted  that  if  the  hydrogen  and  oxygen,  instead 
of  being  at  atmospheric  pressure,  be  at  a  lower  pressure,  the  electro- 
motive force  of  the  cell  will  be  lower.  In  fact,  if  the  pressures  of 
the  gases  be  reduced  almost  to  zero,  the  electromotive  force  will 
nearly  disappear.  Under  such  a  condition  water  may  evidently  be 

1  Ztschr.  phys.  Chem.,  14,  577  (1894). 

2  See,  for  example,  Ztschr.  phys.  Chem.,  55,  473  (1906). 
8  Haber,  Ztschr.  Elektrochemie,  12,  415  (1906). 


ELECTROLYSIS  AND  POLARIZATION  295 

decomposed  by  currents  of  minimum  electromotive  force,  it  being 
only  necessary  to  apply  one  which  exceeds  that  of  the  cell  itself 
by  a  very  small  amount.  From  this  it  is  clear  that  the  electri- 
cal energy  obtainable  through  the  formation  of  water  from  oxygen 
and  hydrogen,  or  necessary  for  its  decomposition  (the  two  being 
equal  and  of  opposite  sign),  may  assume  any  magnitude  from  zero 
to  a  certain  value  dependent  on  the  pressures  of  the  gases  or  their 
concentrations.  The  heats  of  formation  at  constant  pressure,  on  the 
other  hand,  are  independent  of  the  pressure,  within  such  limits  as 
the  gas  laws  hold.  This  is  the  most  direct  evidence  that  a  simple 
relation  cannot  exist  between  the  heat  of  reaction  and  the  electrical 
energy  obtained.  It  is,  however,  possible  in  this  case  to  calculate  the 
amount  of  one  of  these  two  forms  of  energy  from  a  knowledge  of  the 
other  when  the  changes  of  the  temperature  coefficient  due  to  pressure 
changes  are  known. 

That  water  may  thus  be  decomposed  by  minimum  quantities  of 
electrical  energy  seems  at  first  a  contradiction  of  the  law  of  the  con- 
servation of  energy.  This  is,  however,  in  no  wise  the  case.  The 
law  referred  to  declares  that  by  the  reversible  changes  of  a  system 
from  one  condition  to  another,  the  same  amount  of  work  must 
always  be  done,  and  this  condition  exists  in  the  present  case.  The 
decomposition  of  water  into  hydrogen  and  oxygen  at  atmospheric 
pressure  may  be  accomplished,  on  the  one  hand,  by  the  application 
of  electrical  energy  alone.  A  gas  cell  such  as  described,  the  gases 
being  under  atmospheric  pressure,  may  be  used,  an  opposing  electro- 
motive force  just  exceeding  that  of  the  cell  being  connected  with  it. 
Electrical  energy  alone  then  causes  the  decomposition  of  the  water 
into  hydrogen  and  oxygen  at  atmospheric  pressure.  This  same 
result  may,  however,  be  brought  about  in  another  way.  For  instance, 
a  hydrogen-oxygen  cell  in  which  the  pressure  of  the  gases  is  one 
tenth  atmosphere  may  be  employed.  The  electromotive  force  of 
this  cell  being  lower  than  the  previous  one,  less  electrical  energy  is 
required  to  produce  the  hydrogen  and  oxygen  at  the  reduced  pres- 
sure. But  the  work  which  corresponds  to  the  difference  between 
the  two  quantities  of  electrical  energy  employed  must  exactly  suffice 
to  compress  the  gases  produced  at  one  tenth  atmosphere  to  the  pres- 
sure of  one  atmosphere,  and  thus  the  total  work  in  the  two  cases, 
although  done  in  different  ways,  has  remained  the  same. 

When  platinized  electrodes  are  used,  the  formation  and  the  decom- 
position of  the  water  are  reversible.  At  atmospheric  pressure  water 
may  be  decomposed  by  an  electromotive  force  of  1.22  volts.  If  the  elec- 
trodes are  not  platinized,  the  electrolysis  does  not  take  place  until  the 


296  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

electromotive  force  is  1.67  volts.  This  is  the  maximum  value  for  de- 
composition found  for  the  acids  and  bases,  hydrogen  and  oxygen  being 
the  products.  It  was  long  considered  surprising  that  the  decomposi- 
tion point  in  the  latter  case  is  so  high,  notwithstanding  the  fact  that 
only  the  partial  pressure  of  the  atmosphere  is  exerted  upon  each  of 
the  gases.  Furthermore,  the  fact  that  the  decomposition  point 
is  dependent  upon  the  nature  of  the  indifferent  electrode  appeared 
curious. 

These  results  can  now  be  understood.  In  the  first  place,  when 
electrodes  such  as  ordinary  platinum  or  gold l  are  employed,  the 
process  is  no  longer  a  reversible  one.  These  electrodes  have  too  feeble 
absorbing  power  to  remove  the  gases  as  rapidly  as  they  are  formed. 
With  platinized  electrodes  there  is  equilibrium  between  the  gas 
dissolved  in  the  solution,  that  dissolved  in  or  taken  up  by  the 
electrode,  and  the  volume  of  gas  surrounding  the  electrode.  If  the 
applied  electromotive  force  be  great  enough  to  overcome  that  of 
the  gas  cell,  gas  separates  at  the  electrodes,  and  thereby  its  concen- 
tration in  the  solution  as  well  as  in  the  electrode  is  increased.  The 
former  condition  of  equilibrium  is  soon  reproduced,  for  the  electrode 
yields  its  excess  of  gas  to  the  space  about  it  (which  is  considered  so 
great  that  no  change  in  the  concentration  of  this  gas  in  it  is  pro- 
duced), and  in  this  manner  prevents  supersaturation  of  the  liquid. 
The  gas  formed  by  continued  decomposition  of  the  electrolyte  thus 
always  escapes  into  a  space  filled  with  a  gas  at  constant  concentra- 
tion. The  generation  can  therefore  always  take  place  under  the 
same  electromotive  force. 

The  conditions  are  entirely  different  when  the  electrodes  are  of 
gold  or  of  unplatinized  platinum.  These  have  practically  no  absorb- 
ent action  on  the  gases,  and  there  is  thus  no  medium  to  bring  about 
equilibrium  between  the  solutions  of  the  gases  as  formed  in  the  cell 
and  the  gases  in  the  space  about  the  electrodes.  Proceeding  on  this 
assumption,  the  result  of  a  gradually  increasing  electromotive  force 

1  If  carbon  be  used  as  an  electrode,  the  kind  of  carbon  is  an  important  factor. 
Carbon  is  capable  of  taking  up  gases  to  a  considerable  extent,  and  this  property 
increases  its  value  as  positive  electrode  of  a  galvanic  element.  In  the  Le- 
clanch6  element,  for  example,  hydrogen  is  evolved  at  the  carbon  pole,  and  the 
property  of  carbon  just  mentioned  causes  the  gas  to  pass  quickly  from  the  liquid 
to  the  air,  thus  reducing  the  polarization  at  this  electrode.  For  long-continued 
activity  of  the  cell,  the  carbon  is  often  incapable  of  removing  the  hydrogen  with 
sufficient  rapidity,  and  polarization  is  the  result.  If  the  action  of  the  cell  be 
stopped  for  a  time,  the  hydrogen  dissolved  in  the  liquid  has  an  opportunity  to 
escape,  and  the  element,  becoming  thus  depolarized,  again  exhibits  its  original 
electromotive  force,  i.e.  it  recuperates. 


ELECTROLYSIS  AND  POLARIZATION  297 

opposing  such  a  gas  cell  would  be  exactly  as  observed.  Beginning 
with  a  low  electromotive  force,  a  scarcely  perceptible  decomposition 
of  water  would  take  place,  the  concentrations  of  the  hydrogen  and 
oxygen  in  the  water  being  at  first  inconsiderable.  At  each  subse- 
quent increase  of  the  applied  electromotive  force  so  much  water  at 
the  most  may  be  decomposed  that  the  concentration  of  the  gases  in 
solution  at  the  electrodes  is  made  exactly  that  which  would  produce 
an  equivalent  electromotive  force  with  platinized  electrodes.  A 
higher  concentration  of  the  gases  can  evidently  not  be  produced, 
otherwise  perpetual  motion  would  be  possible.  This  explains  the 
temporary  current  observed  in  the  galvanometer.  Diffusion  alone 
causes  disturbances,  the  gases  being  thereby  very  slowly  removed 
from  the  electrodes  and  the  concentration  reduced  so  that  further 
decomposition  takes  place.  The  galvanometer  corroborates  this, 
since,  after  the  first  deflection,  the  needle  does  not  return  quite  to 
its  former  position.  It  thus  indicates  a  slight  residual  current.1 
Upon  gradually  increasing  the  electromotive  force,  the  concentration 
of  the  separated  gases  continually  increases,  until  finally  a  point  is 
reached  at  which  gas  is  evolved.  The  resistance  which  opposes 
the  formation  of  bubbles,  or  another  passive  resistance  of  an  un- 
known nature  which  opposes  the  escape  of  the  gas  into  the  space 
above,  is  then  overcome.  When  this  point  has  been  reached,  water 
may  be  decomposed  without  causing  a  further  increase  in  the  con- 
centration of  the  gases  dissolved  at  or  in  the  electrodes.  The  gases 
are  then  continually  evolved  as  bubbles,  and  the  so-called  decomposi- 
tion point  is  observed,  that  is,  that  point  above  which  water  may  be 
continually  decomposed  without  the  aid  of  diffusion.  The  less  the  dif- 
fusion of  separated  substance  from  the  immediate  neighborhood  of 
the  electrode,  the  more  marked  is  the  decomposition  point,  and  in- 
deed often  (in  the  case  of  metals)  the  galvanometer  exhibits  a  clearly 
defined  sudden  rise  in  the  strength  of  the  current  at  this  point. 

However,  even  this  conception  does  not  embrace  all  actual  relation- 
ships. It  has  been  observed  that  the  decomposition  point  is  not 
always  identical  with  the  point  at  which  bubbles  of  gas  are  formed. 
The  latter  point,  the  observation  of  which  is  to  a  large  degree  sub- 
ject to  chance,  very  often  is  later  than  the  former.  Finally,  it  has 
been  proven  that  the  decomposition  point  is  independent  of  the  pres- 
sure.2 It  must  then  be  assumed  that,  at  the  decomposition  point, 
the  metal  is  saturated  with  gas  to  such  an  extent  that  it  gives  the 
gas  off  to  the  surrounding  liquid  as  rapidly  as  it  is  brought  up  to 

1  Nernst  and  Merriam,  Ztschr.  phys.  Chem.,  53,  235  (1905). 
8  Wulf,  Ztschr.  phys.  Chem.,  48,  87  (1904). 


A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

the  metal  by  a  further  increase  of  the  electromotive  force.  This 
process,  which  takes  place  without  involving  a  change  in  volume,  is 
independent  of  pressure.  From  this,  the  degree  of  the  dependence 
of  the  decomposition  point  on  the  solubility  of  the  separated  gas  in 
the  electrode  is  very  evident.  It  is  also  evident  that  the  greater  the 
solubility  of  the  gas  in  the  liquid,  the  farther  apart  will  be  the 
decomposition  point  and  the  point  at  which  bubbles  appear.  This 
conclusion  is  confirmed  by  experience. 

The  great  influence  of  the  electrode  material  is  shown  by  the  in- 
vestigations of  Coehn  and  Dannenberg,1  and  Caspari.2  The  former 
two  investigators  determined  the  decomposition  points  at  cathodes 
of  various  metals,  for  the  most  part,  in  a  normal  solution  of  sulfuric 
acid.  If  the  potential-difference  at  the  reversible  platinized  plati- 
num electrode  be  placed  equal  to  zero,  the  results  obtained  by  them 
are  as  follows :  — 


METAL 

DECOMPOSITION  VOLTAGE 
(EA  electrode—  electrolyte) 

Palladium        ....     .;>•';•      •     /  •        • 

+  0.26  volt 

Platiaum         ........ 

-  0.00  volt 

Iron         

-  0.03  volt 

Gold        

-  0.05  volt 

Silver       

-  0.07  volt 

Nickel      

-  0.14  volt 

Copper    

-0.19  volt 

Aluminium      .         .      -  v        «,-».*        *        *  •; 

-  0.27  volt 

Lead        .        .        ......        . 

-  0.36  volt 

Mercury          

-  0.44  volt 

Only  in  the  case  of  palladium  is  the  separation  of  hydrogen  facili- 
tated, and  this  is  most  certainly  due  to  the  formation  of  an  alloy. 
In  all  the  other  cases,  a  considerable  retardation  or  hindrance  of  the 
separation,  or  in  other  words  a  considerable  over-voltage,  exists.  This 
over-voltage  appears  to  be  greatest  in  the  case  of  metals  which  pos- 
sess the  smallest  occlusion  capacity. 

In  the  case  of  the  cathodic  polarization  of  metals  in  a  solution  of 
potassium  hydroxide  it  was  found  that  the  order  of,  and  the  differ- 
ences between,  the  decomposition  voltages  are  the  same  as  those  given 
above.  From  this  it  is  to  be  concluded  that  no  alkali-alloy  is  formed 
at  the  decomposition  point,  but  only  a  separation  of  hydrogen  takes 
place.  Mercury  at  no  time  left  its  place  in  the  above  order,  and 

1  Ztschr.phys.  Chem.,  38,  609  (1901). 

2  Ztschr.phys.  Chem.,  30,  89  (1899). 


ELECTROLYSIS  AND  POLARIZATION  299 

only  when  high  potential-differences  are  reached  is  the  phenomenon 
of  disintegration  or  powdering  of  the  cathode,  as  in  the  case  of  tin 
and  lead,  which  was  studied  by  Haber,  Sack,1  and  Bredig,  observable. 
This  behavior  of  tin  and  lead  is  explained  on  the  assumption  of  the 
formation  of  an  alkali  alloy. 

If,  as  in  Caspari's  work,  the  electromotive  force  which  is  required 
to  produce  a  visible  evolution  of  gas  be  determined,  the  values  will 
be  found  to  be  somewhat  greater  but  in  the  same  order  as  those  in 
the  above  table.  His  highest  values,  obtained  with  zinc  and  mercury, 
are  —  0.70  and  —  0.76  volt,  respectively. 

These  values  are  of  interest  in  connection  with  the  chemical  solu- 
tion of  metals  in  acids.  It  may  be  seen  from  the  table  given  on 
page  248  that  zinc  tends  to  separate  from  a  normal  solution  of 
hydrogen  ions  with  an  intensity  of  0.80  of  a  volt.  Therefore,  since 
the  over-voltage  is  equal  to  0.70  of  a  volt,  zinc  dissolves  in  a  solution 
which  is  normal  in  respect  to  the  hydrogen  and  zinc  ions  only  very 
slowly.  By  increasing  the  concentration  of  the  zinc  ions,  as,  for 
example,  by  the  addition  of  zinc  sulphate,  the  solution  of  the  zinc 
may  be  made  even  slower  or  brought  to  a  standstill,  while  by 
increasing  the  concentration  of  the  hydrogen  ions,  or,  what  is  the 
same  thing,  of  the  acid,  the  action  may  be  accelerated. 

Commercial  zinc  possesses  a  smaller  over-voltage,  and  therefore  is 
more  easily  dissolved  than  is  pure  zinc.  If  it  be  amalgamated,  it 
dissolves  less  easily  and  its  over-voltage  increases ;  while  if  pure  zinc 
be  amalgamated,  the  ease  with  which  it  dissolves  and  its  over-voltage 
do  not  suffer  any  considerable  change. 

Not  only  in  the  case  of  hydrogen,  but  also  in  that  of  oxygen,  an 
over-voltage  which  varies  with  the  nature  of  the  electrode  (in  this 
case  the  anode)  is  produced  by  the  separation  of  the  gas.  Coehn 
and  Osaka,2  making  use  of  a  normal  solution  of  potassium  hydroxide 
as  an  electrolyte,  measured  the  anode  voltage  against  a  constant 
hydrogen  electrode  which  was  also  in  contact  with  a  normal  solution 
of  potassium  hydroxide.  The  values  obtained  by  them  are  given  in 
the  table  on  the  following  page. 

It  should  be  noted  that  the  decomposition  point  in  this  case  is  iden- 
tical with  that  at  which  visible  evolution  of  oxygen  takes  place  and 
that  the  order  of  the  metals  is  quite  different  from  that  in  the  case  of 
the  hydrogen.  The  results  given  here  indicate  that  the  commercial 
decomposition  of  water  could  be  carried  out  with  the  least  expendi- 
ture of  energy  with  the  use  of  nickel  electrodes. 

1  Ztschr.  anorg.  Chem.,  34,  286  (1903). 

2  Ztschr.  anorg.  Chem.,  34,  86  (1903). 


300 


A   TEXT-BOOK   OF   ELECTRO-CHEMISTRY 


METAL 

DECOMPOSITION  VOLTAGE 

Gold         
Platinum  (polished)         

1.75 
1.67 

Palladium        ........ 
Cadmium         
Silver       :                                  
Lead       
Copper    
Iron         

1.65 
1.65 
1.63 
1.53 
1.48 
1.47 
1.47 

Cobalt     .        .        .      •:,'!      A  .    > 
Nickel  (blank)        .        . 

1.36 
1.35 

Nickel  (spongy)     .... 

1.28 

Even  with  the  same  substance  used  as  an  anode  the  decomposition 
value  varies  with  the  treatment  to  which  the  substance  has  been 
subjected,  i.e.  with  its  previous  history.  This  was  mentioned  on 
page  296  in  reference  to  carbon.  This  subject  will  be  further  con- 
sidered later  on. 

Both  bromine  and  iodine  separate  reversibly  at  platinum  anodes. 

It  may  be  questioned  whether  the  order  of  the  over-voltages  ob- 
tained under  practically  zero-current  conditions  is  the  same  as  the 
order  which  is  obtained  during  electrolysis  with  a  high  current 
density.  Furthermore,  is  the  latter  series  of  values  noticeably  higher 
than  the  former  ?  These  questions  have  been  investigated  by  Tafel.1 
The  maximum  values  thus  far  obtained  are  given  in  the  following 
table.  They  were  obtained  at  12°  in  a  2-normal  sulfuric  acid 


METAL 

OVER-VOLTAGES  (FA) 

1.30 

Lead  (polished)          

1.30 

Lead  (rough)      
Cadmium    

1.23 
1.22 

Tin    

1.15 

Bismuth      

1.00 

Gold    

0.95 

Silver  

0.93? 

0.79 

Nickel         ....               

0.74 

0.07 

^Ztschr.  phys.  Chem.,  50,  712  (1905).  The  change  in  potential  due  to  the 
change  in  the  concentration  of  H  ions  at  the  electrodes  is,  as  the  experiments 
•with  platinized  platinums  show,  negligible. 


ELECTROLYSIS  AND  POLARIZATION  301 

solution  with  a  current  density  maintained  constant  at  0.1  of  an 
ampere  per  square  centimeter  of  electrode  surface.  The  anode  sec- 
tion was  separated  from  the  cathode  section. 

It  should  be  noted  that  the  value  of  the  over-voltage  for  a  given 
current  density  is  for  many  metals  dependent  on  the  previous  treat- 
ment to  which  the  electrode  has  been  subjected,  as  for  example,  upon 
the  current  density  maintained  when  the  cathode  was  previously 
polarized.  The  over-voltage  of  all  metals  changes  slowly  as  time 
passes.  This  change  and  the  dependence  of  the  potential  on  specific 
influences  is  not  the  same  for  different  metals.  An  access  of  the 
anode  solution  to  the  cathode  compartment  generally  lowers  the 
potential-difference.  The  maximum  value  of  the  potential-differ- 
ence is  reached  at  once  with  mercury  and  lead,  but  very  slowly  with 
copper,  nickel,  and  gold,  and  not  at  all  with  polished  platinum.  The 
potential  decreases  with  increasing  temperature. 

The  investigations  of  Forster  and  Muller, l  and  Forster  and  Piguet,2 
of  anode  potentials  in  2-normal  potassium  hydroxide  show  relation- 
ships similar  to  the  above. 

Finally,  it  should  be  mentioned  that  E.  Muller 3  has  found  that 
the  over-voltage  at  the  anode,  in  the  case  of  platinum,  is  greatly 
increased  by  the  addition  of  fluorine  ions.  It  follows  from  this  fact 
and  also  from  the  above-mentioned  work  of  Tafel  that  the  over- 
voltage  depends  also  on  the  nature  of  the  electrolyte. 

According  to  the  explanations  already  given,  the  electromotive 
force  of  the  hydrogen-oxygen  cell  is  dependent  upon  the  concentra- 
tions of  the  gases,  but  nearly  independent  of  the  nature  of  the  elec- 
trolyte. The  electrolyte  may  almost  equally  well  be  an  acid  or  a  base. 
The  electromotive  force  is  the  sum  of  the  potential-differences  pro- 
duced at  the  hydrogen  and  oxygen  electrodes.  That  of  the  former  is 
dependent  upon  the  concentration  of  the  hydrogen  ions,  that  of  the 
latter  upon  the  concentration  of  the  hydroxyl  ions,  for  a  given  con- 
centration of  the  gases.  According  to  the  law  of  mass  action,  the 
product  of  the  concentrations  of  the  hydrogen  and  hydroxyl  ions  is 
(nearly)  always  constant  without  regard  to  other  substances  present; 
therefore,  although  the  values  of  the  single  potential-differences  may 
vary  considerably  on  changing  the  homogeneous  solution,  their  sum 
always  remains  the  same.4 

Leaving  out  of  account  metal  salt  solutions  reducible  by  hydrogen, 

lZtschr.  Elektrochem.,  8,  527  (1902). 

*Ztschr.  Elektrochem.,  10,  714  (1904). 

*Ztschr.  Elektrochem.,  10,  753  (1904). 

4  For  further  particulars  see  L.  Glaser,  Ztschr.  Electrochem.,  4,  355  (1898). 


302  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

and  chlorides,  bromides,  iodides,  etc.,  reducible  by  oxygen,  the  ions 
of  water  alone  take  part  in  the  decomposition,  instead  of  those  of  the 
dissolved  electrolyte,  so  that  with  the  limitations  given,  the  principle 
may  be  expressed :  In  electrolysis  a  primary  decomposition  of  the  water 
takes  place.  The  actual  electrical  conductance  is  brought  about  by 
all  the  ions  in  the  solution,  but  at  the  electrode  that  action  takes 
place  which  proceeds  most  easily,  and  this  is  usually  the  separation 
of  the  hydrogen  and  hydroxyl  ions.  When,  for  example,  a  solution 
of  potassium  sulphate  is  being  electrolyzed,  and  the  current  is  not 
too  strong,  there  is  no  reason  for  assuming  the  separation  of  potas- 
sium and  the  S04  radical  at  the  electrodes,  and  the  subsequent  or 
secondary  action  of  these  upon  the  water.  The  fact  that  every  acid 
and  base,  in  so  far  as  they  do  not  possess  a  lower  decomposition 
voltage,  decomposes  at  1.67  volts  can  scarcely  be  otherwise  explained 
than  by  the  assumption  that  in  every  case  the  same  process  takes 
place.  If  a  secondary  action,  i.e.  a  separation  of  the  radicals  at  the 
electrodes  and  a  subsequent  reaction  of  these  with  the  water,  takes 
place,  it  would  be  expected  that  the  decomposition  point  would  not 
be  the  same  in  all  cases  but  would  vary  with  the  velocity  of  the 
action.  In  the  case  of  acetic  acid,  for  example,  a  higher  potential 
would  be  expected,  since  during  electrolysis  of  it  with  a  strong  cur- 
rent only  a  small  quantity  of  oxygen  is  found  mixed  with  the  gas 
evolved  at  the  anode.  The  reaction, 

4  CH3COO'  +  2  H20  =  4  CH3COOH  +  02, 

must  therefore  take  place  slowly.  Whether  or  not  a  primary  de- 
composition of  water  takes  place  when  strong  currents  are  used 
evidently  depends,  for  a  given  concentration,  on  the  velocity  of  the 
formation  of  hydrogen  and  hydroxyl  ions  from  undissociated  water. 
This  subject  will  be  touched  upon  again. 

It  should  be  emphasized  that  the  assumption,  made  earlier,  that 
the  ions  carried  to  the  electrode  by  the  electric  current  always  sep- 
arate on  the  electrode  directly  and  then  react  with  water  or  other 
substances  does  not  appear  to  be  in  agreement  with  facts.  That 
the  conduction  of  the  electric  current  and  the  decomposition  of 
the  electrolyte  at  the  electrodes  are  not  as  closely  related  as  was 
formerly  supposed  is  evident  from  the  simple  fact  that  during  the 
electrolysis  of  every  electrolyte  more  ions  are  separated  at  each 
electrode  than  are  brought  to  it  by  migration  (see  page  67).  Hence 
in  every  case  some  of  the  ions  originally  in  the  solution  near  the 
electrodes  which  have  not  taken  part  in  the  conduction  of  the  current 
are  deposited. 


ELECTROLYSIS  AND  POLARIZATION  303 

The  following  conception,  which  has  already  been  mentioned 
briefly,  appears  to  me  to  be  decidedly  preferable  to  that  formerly 
accepted.  The  conduction  of  the  electric  current  and  the  chemical 
changes  or  separations  at  the  electrodes  are  not  closely  related.  All 
of  the  ions  in  the  solution  take  part  in  the  conduction  of  the  electric  cur- 
rentj  but  only  those  ions  the  separation  of  which  require  the  least  expen- 
diture of  work  or  energy  are  deposited  or  separated  at  the  electrodes. 
Thus  it  may  happen  that  ions  which  conduct  scarcely  a  measurable 
part  of  the  current  play  the  most  important  part  in  the  chemical  de- 
compositions at  the  electrodes,  in  so  far  as  they  are  formed  with 
sufficient  rapidity. 

The  following  example  is  well  adapted  to  show  the  greater  sim- 
plicity of  the  newer  conception.  Suppose  that  a  fairly  concentrated 
solution  of  a  mixture  of  potassium,  cadmium,  copper,  and  silver  salts 
be  electrolyzed  with  a  moderate  current  between  platinum  electrodes. 
In  conducting  the  electric  current,  potassium,  cadmium,  hydrogen, 
copper,  and  silver  ions  migrate  to  the  cathode.  At  the  cathode, 
from  actual  experiment,  it  is  known  that  the  silver  is  first  deposited. 
This  deposition  goes  on  until  the  number  of  silver  ions  remaining  is 
no  longer  sufficient  for  the  current  density  maintained,  when  the 
copper  begins  to  separate  in  the  same  manner.  Following  copper, 
cadmium,  and  finally  hydrogen,  is  deposited.  Is  not  the  simplest 
conceivable  explanation  of  these  experimental  results  that  given  in 
the  following  statement  ? 

Those  ions  separate  first  which  give  up  their  electric  charges  most 
easily.  The  other  ions  must  ivait  their  turn  in  the  order  of  their  ease  of 
deposition.  The  process  takes  place  smoothly  and  comprehensively. 

The  other  conception  may  now  be  applied  to  the  same  process. 
According  to  this  conception,  potassium,  cadmium,  hydrogen,  copper, 
and  silver  ions  separate  simultaneously  at  the  cathode.  The  potas- 
sium may  then  set  free  hydrogen  from  the  water,  cadmium  from  the 
cadmium  salt,  copper  from  the  copper  salt,  and  silver  from  the  silver 
salt.  This  must  be  considered  to  take  place,  for  the  assumption 
cannot  well  be  made  that  there  is  always  a  particle  of  silver  ready  to 
be  precipitated  in  the  immediate  vicinity  of  each  particle  of  potas- 
sium. The  potassium  must  then  separate  those  ions  of  whatever 
kind  which  happen  to  be  in  its  vicinity.  Of  these  substances  sepa- 
rated by  the  potassium,  the  hydrogen  sets  free  cadmium  from  the 
cadmium  salt,  copper  from  the  copper  salt,  and  silver  from  the  silver 
salt.  Of  this  group  of  separated  metals,  the  cadmium  may  set  free 
copper  from  the  copper  salt,  and  silver  from  the  silver  salt.  Finally, 
the  copper  sets  free,  or  deposits,  silver  from  the  silver  salt.  The 


304  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

final  result  of  all  this  is  that  as  long  as  sufficient  silver  is  present,  it 
alone  is  deposited  permanently  on  the  cathode.  This  conception  of 
the  process  of  electrolysis  certainly  cannot  be  said  to  be  as  simple  as 
the  one  given  above,  and  it  involves  the  assumption  of  all  these  sec- 
ondary reactions  which  no  one  has  ever  observed.  The  question  at 
once  arises,  why  make  this  complicated  assumption  when,  as  has 
been  shown,  it  can,  with  greater  simplicity,  be  avoided  ? 

After  this  discussion,  the  values  obtained  during  the  determination 
of  the  decomposition  voltage  with  the  use  of  platinized  platinum 
electrodes  is  easily  understood.  Those  substances  which  decompose 
water  will  be  considered  first.  Both  acids  and  bases  must  have  the 
same  value,  since,  as  already  stated,  the  product  of  the  concentrations 
of  the  hydrogen  and  hydroxyl  ions  at  the  electrodes,  and  conse- 
quently the  sum  of  the  potential-differences  at  the  electrodes,  is  the 
same  in  the  two  cases.  In  the  case  of  salts,  higher  values  should  be 
obtained,  since  at  the  cathode  a  base  is  formed  whereby  the  concen- 
tration of  the  hydroxyl  ions  is  greatly  increased,  with  the  conse- 
quent driving  back  of  the  concentration  of  the  hydrogen  ions  and 
increase  of  the  potential-difference.  A  similar  line  of  reasoning 
holds  for  the  anode  at  which  acid  is  formed,  increasing  the  con- 
centration of  the  hydrogen  and  decreasing  that  of  the  hydroxyl  ions. 
The  less  the  dissociation  of  the  acid  or  base  formed,  the  less  the 
increase  in  the  potential-difference.  This  has  been  observed  to  be 
the  case. 

Since  that  ion  is  always  separated  at  the  electrode  which  requires 
the  least  electromotive  force  for  its  separation,  no  ions  other  than 
hydrogen  and  hydroxyl  ions  (providing  the  concentrations  of  the 
latter  are  sufficiently  great)  come  into  consideration  except  when  the 
electromotive  force  required  for  their  separation  is  less  than  that 
required  for  the  separation  of  hydrogen  and  hydroxyl  ions.  For  this 
reason,  the  decomposition  voltage  of  the  halogen  acids,  etc.,  which 
do  not  cause  a  separation  of  oxygen  is  lower  than  that  of  those  acids 
which  do  cause  the  separation  of  oxygen.  Furthermore,  while  in 
the  case  of  acids  and  bases  which  are  decomposed  with  the  separa- 
tion of  hydrogen  and  oxygen,  the  decomposition  voltage  is  indepen- 
dent of  the  concentration  (since  the  product  of  the  concentrations  of 
the  hydrogen  and  hydroxyl  ions  remains  the  same),  in  the  case  of 
the  halogen  acids  the  decomposition  voltage  rises  with  decreasing 
concentration,  since  an  increase  in  the  concentration  of  the  hydroxyl 
ions  takes  place  corresponding  to  the  decrease  in  that  of  the  hydro- 
gen and  of  the  halogen  ions.  A  dilution  is  finally  reached  at  which 
oxygen  is  continuously  evolved  more  easily  than  is  the  halogen.  At 


ELECTROLYSIS  AND  POLARIZATION  305 

this  dilution,  the  decomposition  voltage  is  equal  to  that  of  water. 
Such  a  case  has  been  realized  with  hydrochloric  acid. 

In  the  foregoing  pages  the  current-voltage  curve  of  any  electrolyte 
has  always  been  discussed  as  if  there  existed  but  a  single  decomposi- 
tion value  which,  by  means  of  measurements  with  an  auxiliary  elec- 
trode, can  be  divided  into  an  anode  and  a  cathode  potential-difference. 
The  recent  measurements  of  Nernst,1  Glaser,2  Bose,3  Coehn  (loc.  cit.)9 
and  others  have  shown  that,  when  the  measurement  is  more  accu- 
rately made,  more  than  one  decomposition  point  may  be  found  under 
certain  circumstances.  Such  measurements  may  best  be  made  as 
follows :  The  electrode  being  investigated,  together  with  any  other 
electrode,  a  galvanometer,  and  an  electromotive  force  which  is 
changeable  at  will,  are  introduced  into  a  circuit.  The  electrode  in 
question  is,  furthermore,  combined  with  an  auxiliary  nonpolarizable 
electrode.  Now  in  obtaining  the  current-  (or  better,  current  density-) 
voltage  curve,  the  electromotive  forces  of  the  cell, 

Auxiliary  electrode  —  Unknown  electrode, 

are  taken  as  the  voltage  values.  With  this  arrangement,  the  nature 
of  the  third  electrode  does  not  come  into  consideration  because  the 
same  electromotive  force  always  corresponds  to  a  definite  current 
density  (referred  to  the  unknown  electrode)  for  a  given  solution.  By 
making  the  unknown  electrode  changeable,  it  is  possible  by  this 
method  to  isolate  better  than  formerly  the  processes  which  take  place 
at  the  anode  and  the  cathode,  respectively.  It  has  been  possible 
with  the  use  of  platinum  electrodes  to  establish  two  anodic  decom- 
position values,  namely, 

ZA=1.14  and  =  1.67  volts, 
but  only  one  cathodic  value, 

2h= 0.0  volt, 

for  a  1  normal  solution  of  an  acid. 

The  question  now  arises,  how  can  the  existence  of  this  lower  value 
of  the  decomposition  point  of  water  be  explained  ?  In  addition  to 
the  assumption  previously  made  that  the  decomposition  potential 
of  1.67  volts  is  the  result  of  supersaturation  phenomena,  and,  as 
observed,  varies  with  the  material  of  which  the  electrode  is  com- 
posed, it  may  be  stated  that  even  ordinary  platinum  electrodes  pos- 

i  Ber.,  30,  1647  (1897).          2  Ztschr.  Electrochem.,  4,  355  (1898). 
*Ztschr.  mectrochem.,  5,  153  (1898). 


306  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

sess,  although  a  very  slight,  yet  a  sufficient  degree  of  reversibility  to 
produce  a  continuous  decomposition  at  1.14  volts  which  is  distinctly 
detected  by  very  exact  measurements.  The  reversibility  may  be  due 
to  the  formation  of  an  intermediary  compound  between  oxygen  and 
water.  The  decomposition  value  of  1.14  volts  is  that  of  the  reversi- 
ble reaction, 

4  OH'  +  4  Q  +    ^t  4  OH     ±  2 


when  the  oxygen  is  at.  atmospheric  pressure  and  the  hydrogen  ion 
concentration  is  1  normal. 

The  lower  anodic  decomposition  value  then  corresponds  to  a  rever- 
sible process,  while  the  higher  value  is  plainly  due  to  the  supersatura- 
tion  phenomena.  This  is  in  agreement  with  the  fact  that  the  former 
value  is  independent1  of,  and  the  latter  value  dependent  upon,  the 
electrode  material.  The  process  corresponding  to  the  value  1.67 
volts  may  be  represented  as  follows  :  — 

40H'+  4Q  (+)  ^±  4  OH  5±  H20  +  02  ->  02, 

where  02  represents  traces  of  oxygen  dissolved  to  a  high  concentra- 
tion, and  O2  ,  oxygen  at  atmospheric  pressure.  The  part  of  the  pro- 
cess indicated  by  the  single  arrow  can  proceed  in  but  one  direction 
and  is  accompanied  by  a  loss  in  free  energy. 

It  might  be  expected  that  metals  which  exhibit  a  considerable 
over-voltage  in  respect  to  the  separation  of  hydrogen  would  also  give 
a  reversible  cathodic  decomposition  point  at 

FA  —  0.0  volt 

in  a  solution  of  1  normal  concentration  in  respect  to  hydrogen 
ions.  Up  to  the  present  time,  however,  this  has  not  been  found  to 
be  the  case. 

It  has  been  endeavored  to  explain  the  existence  of  the  two 
decomposition  values  given  above  in  another  manner,  based  partly 
on  the  assumption,  which  is  certainly  theoretically  justifiable,  that 
there  are  present  in  the  water  oxygen  as  well  as  hydroxyl  ions.  In 
this  connection  see  note  on  page  254.  It  seems  to  me  that,  in  order 
to  explain  this  electrolytic  phenomenon,  it  is  not  necessary  to 
involve  the  oxygen  ions  which  are  present,  if  at  all,  in  a  very  small 
concentration.  In  the  case  of  the  electrical  phenomenon  under  con- 
sideration, it  does  not  appear  advisable  to  involve  in  the  explanations 

1  In  view  of  the  irregularities  of  the  oxygen  electrode  mentioned  on  page  296, 
there  cannot  be  a  complete  independence  of  the  material  of  the  anode. 


ELECTROLYSIS  AND  POLARIZATION  30T 

such  slight  concentrations  as  those  of  the  0  ions.  Haber l  has  with1 
reason  pointed  out  that  there  are  considerable  objections  to  the 
assumption  of  even  a  moderate  velocity  of  formation  of  ions  in  the 
case  of  such  extremely  small  ion  concentrations.  This  point  of  view 
must  always  be  taken  into  consideration  in  reference  to  electrolysis. 
If  by  means  of  the  formation  of  a  complex  compound,  or  otherwise, 
the  concentration  of  an  ion  falls  below  a  certain  value,  the  separation 
of  this  free  ion  at  the  electrode  is  no  longer  to  be  assumed.  Finally, 
the  results  of  the  experiments  of  Hofer  and  Moest 2  also  lead  to  the 
assumption  of  the  discharge  of  OH  ions  at  the  anode.  They  found 
that,  during  the  electrolysis  of  such  mixtures  as  that  of  sodium 
acetate  and  sodium  sulfate,  besides  ether  and  carbon  dioxide,  methyl 
alcohol  was  formed  in  considerable  quantities  at  the  anode.  This 
formation  of  methyl  alcohol  can  scarcely  be  explained  otherwise 
than  on  the  assumption  of  a  direct  union  of  OH-  and  CH3-radicals. 

By  the  very  recent  investigations  of  Grafenburg,3  Brand,4  and 
Luther  and  Inglis 5  it  has  been  demonstrated  that  the  electromotive 
force  of  an  ozone-hydrogen  cell  at  atmospheric  pressure  and  room 
temperature,  using  a  1  normal  acid  solution,  is  equal  to  1.66  volts. 
The  cell  is,  moreover,  reversible.  Consequently,  in  the  case  of  the 
anode  potential, 

?ft=  1.66  volts, 

we  have  a  third  characteristic  point  which  corresponds  to  a  re- 
versible process  and  which  is  also  independent  of  the  nature  of  the 
material  of  the  noble  anode.  In  the  case  of  platinum  this  point  is 
nearly  identical  with  the  second  decomposition  point  already 
mentioned.  At  the  present  time  it  is  not  possible  to  give  a  scheme 
representing  the  electrolytic  formation  or  decomposition  of  ozone. 

Finally,  there  is  another  result  obtained  in  the  investigation  men- 
tioned on  page  305  which  is  of  great  interest.  It  was  found  that  still 
other  anode  decomposition  values  may  be  detected  above  the  value 
1.67  volts.  When  sulfuric  acid,  for  example,  is  electrolyzed  between 
platinum  electrodes,  four  such  values  have  been  found,  namely, 

£A  electrode-electrolyte  =  1-14;    1.67;    1.95;    and  2.6  VOltS. 

At  each  of  these  points,  the  electrolysis  receives  a  sudden  accelera- 
tion. A  similar  behavior  may  also  be  observed  in  the  case  of  bases. 
These  results  seem  to  indicate  that  other  ions  besides  hydrogen  and 

1  Ztschr.  Elektrochem.,  10,  443  and  773  (1904).      *  Drud.  Ann.,  9,  468  (1902). 

2  Liebigs  Ann.,  323,  304  (1902).  6  Ztschr.  phys.  Chem.,  43,  203  (1903). 
8  Ztschr.  Elektrochem.,  8,  297  (1902). 


308 


A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 


hydroxyl  ions  take  part  in  the  electrolysis.  It  would  seem  probable 
that  the  value  1.95  volts  corresponds  to  that  point  at  which  the  sulf  ate 
ions,  and  the  value  2.6  volts  to  that  at  which  the  acid  sulfate  ions, 
begin  to  take  part  in  the  electrolysis.  It  may  further  be  concluded 
from  these  results  that  the  velocity  of  formation  of  hydrogen  and 
hydroxyl  ions  cannot  be  especially  great,  for  otherwise  it  would  not 
have  been  possible  to  find  the  above  decomposition  points.  This 
leads  to  the  conclusion  that  the  hydrogen  and  oxygen  set  free  by 
the  action  of  strong  electric  currents  is,  to  a  great  extent,  of  second- 
ary origin,  resulting  from  the  action  of  the  liberated  radicals  on  the 
water. 

In  the  following  table  the  values  of  the  anodic  decomposition 
voltage, 

£*  electrode -electrolyte, 

(except  at  the  point  1.14  volts)  for  a  number  of  acids  are  given :  — 


ACID 

Cn 

DECOMPOSITION  VOLTAGES 

First 

Second 

Third 

Nitric     .... 

2.3 
2.3 
3.5 
3.5 
3.5 
3.5 
3.5  • 
1.2 
saturated 
saturated 

1.66 
1.67 
1.69 
1.67 
1.68 
1.67 
1.67 
1.66 
1.67 
1.68 

1.88 
1.96 
1.88 
2.05 
2.20 
2.35 

1.85 
2.00 
1.97 

2.18 

2.2 

2.6 

Phosphoric 

Formic  

Acetic    

Propionic  

Butyric       

Valerianic       

Tartaric     

Benzoic 

Phthalic     . 

The  assumption  just  made  that  each  decomposition  voltage,  or, 
in  other  words,  each  factor  of  irregularity  of  the  current-voltage 
curve,  indicates  that  a  new  reaction  is  beginning  to  take  place  is,  in 
a  way,  confirmed  by  the  investigation  of  Bose  (loc.  cit.,  Figure  51).  As 
an  electrolyte,  he  used  a  0.965  normal  solution  of  hydrochloric  acid 
to  which  various  quantities  of  potassium  bromide  had  been  added. 
When  the  bromine  ion  concentration  was  large,  he  obtained  but  one 
anode  decomposition  point,  namely,  that  of  the  bromine  ions.  Like- 
wise when  the  bromine  ion  concentration  was  small,  only  a  single 
value  was  obtained,  this  time  that  of  the  chlorine  ions.  Only  at  a 
definite  concentration  of  the  bromine  ions  (0.001  n.  KBr)  did  he 
obtain  both  the  value  for  bromine  ions  and  that  for  chlorine  ions 


ELECTROLYSIS  AND  POLARIZATION 


309 


(see  the  two  breaks  in  curve  IV).  Between  these  two  turning 
points  the  curve  follows  first  a  vertical,  then  a  moderately  upward 
sloping  direction,  which  in  many  cases  becomes  completely  horizon- 
tal and  even  may  slope 

downward  again.  It  is  ANODIC  CURVES  FOR  Br  AND  Cl  SEPARATION 
assumed  that  the  curve  FR°M  HC1  CONTAINING  SOLUTIONS  OF  KBr 
follows  such  a  horizontal 
course  when  the  primary 
substance  which  is  disap- 
pearing during  the  elec- 
trolysis is  nearly  con- 
sumed at  the  electrodes.1 
To  be  sure,  it  should  be 
taken  into  consideration 
that  in  these  experiments 
the  appearance  of  a  new 
turning  point  in  the  curve 
is  accompanied  by  the  ap- 
pearance of  a  new  phase 
at  the  electrode,  while  in 
earlier  cases  a  new  phase 
could  not  be  detected. 

The  significance  of  the  former  turning  points  is,  therefore,  not  yet 
established  with  certainty.  However,  according  to  Luther  and  Bris- 
lee 2  it  is  possible  that  in  many  cases  the  different  turning  points  do 
not  correspond  to  different  processes  taking  place  in  the  electrolyte, 
but  to  different  changes  taking  place  as  time  passes  on  the  surface  of 
the  electrode.  This  agrees  with  the  remarks  made  on  page  301  in 
regard  to  the  potential  of  the  electrodes. 


Solvent 

=  0.965  HC1 

Sol.  I  = 

1.0  KBr 

Sol.  II  = 

=  0.1  KBr 

1 

Sol.  Ill 
Sol.  IV 

=  0.01  KBr        1 
=  0.001  KBr      1 

c 

Sol.  V  = 

=  0.0001  KBr    l|  H 

HI     V 

F     ,  J    . 

1  J 

*v  v  o  r«v  ••«     i      i.**— 

Bromine  Separation  { 

Chlorine  Separation 

FIG.  51 


IMPORTANCE  OF  THE  DECOMPOSITION  VOLTAGE  IN  MAK- 
ING ELECTROLYTIC  SEPARATIONS  AND  IN  PREPARING 
NEW  COMPOUNDS 

As  already  shown,  different  decomposition  points  characterize  the 
various  metals.  From  this  fact  it  was  inferred  by  Le  Blanc  that  it 
should  be  possible  to  quantitatively  precipitate3  metals  one  after 
another  from  their  mixed  solutions  by  a  gradual  increase  in  the 

1  See  also  the  recently  published  investigation  of  F.  Weigert,  Ztschr.  Elektro* 
chem.,  12,  377  (1906). 

2  Ztschr.  phys.  Chem.,  12,  97  (1893). 

8  Ztschr.  phys.  Chem.,  45,  216  (1903). 


310  A  TEXT-BOOK  OF   ELECTRO-CHEMISTRY 

electromotive  force  of  the  decomposing  current  That  this  may  be 
done  has  been  shown  by  Freudenberg.1 

If  through  a  solution  containing  salts  of  copper  and  cadmium  a 
current  be  passed,  the  electromotive  force  of  which  is  insufficient  for 
the  continuous  deposition  of  the  cadmium  but  capable  of  precipitat- 
ing the  copper,  the  latter  metal  alone  is  completely  precipitated. 
When  all  the  copper  is  precipitated  the  current  ceases,  it  being  thus 
unnecessary  to  pay  attention  to  the  electrolysis.  The  electromotive 
force  necessary  for  the  precipitation  of  the  copper  increases  with  the 
dilution  of  the  solution,  according  to  the  formula, 

RT,    P 

F  = In  - ; 

VQ      P 

but  since  an  increase  in  dilution  from  ^  to  ^ooooo  normal  (the 
limit  of  analytical  determinations)  causes  an  increase  of  less  than 
0.3  volt  for  a  monovalent  and  half  as  much  for  a  divalent  metal, 
this  does  not  hinder  the  separation  if  the  solution  pressures  differ 
moderately  from  each  other. 

After  the  precipitation  of  the  copper  the  electromotive  force  may 
be  increased  and  the  cadmium  precipitated.  In  this  way  a  number 
of  separations  have  become  possible,  which  had  not  succeeded  when 
attention  was  given  to  changing  the  current-strength  instead  of  the 
electromotive  force.  In  the  future  this  must  be  kept  in  mind  in  all 
processes  of  electrolysis.  Complications  may,  however,  arise  through 
the  formation  of  alloys  or  of  chemical  compounds,  which  may  pre- 
vent a  complete  separation. 

Besides  the  neutral  or  acid  solutions,  those  of  the  double  com- 
pounds of  the  metal  salt  with  ammonium  oxalate  or  potassium 

1  It  should,  however,  be  noted  that  about  ten  years  ago  M.  Kiliani  called  atten- 
tion to  the  possibility  of  electrolytic  separations  by  a  gradation  of  the  electro- 
motive force,  and  carried  out  the  separation  of  silver  and  copper.  He  came 
upon  the  idea  in  considering  the  heat  effects  characterizing  individual  metals, 
and  calculated  from  them  the  electrical  energy  necessary  for  their  precipitation. 
This  method  of  calculation  has  been  shown  to  be  inapplicable,  for  which  reason, 
and  perhaps  more  especially  because  of  the  general  uncertainty  regarding  polar- 
ization conditions  introduced,  his  work  did  not  receive  much  attention.  That 
when  the  electromotive  force  is  above  a  certain  value  a  metal  may  be  continuously 
precipitated  from  its  solution,  while  below  this  point  only  an  analytically  negli- 
gible or  absolutely  unweighable  amount  precipitates,  was  not  at  that  time  clear. 
The  opinion  was  then  much  more  commonly  held  that  even  with  low  electro- 
motive forces  not  inconsiderable  quantities  of  the  metal  were  precipitated, 
according  to  which  view  the  separation  of  two  metals  by  a  proper  regulation 
of  the  electromotive  force  appeared  as  an  accident  rather  than  as  a  necessary 
result  of  recognized  relations. 


ELECTROLYSIS  AND  POLARIZATION  311 

cyanide  are  especially  adapted  to  such  separations.  In  the  latter 
many  inetals  can  be  separated  from  one  another  which  cannot  be  sep- 
arated in  acid  solution.  Thus  in  acid  solution  platinum  cannot  be 
separated  from  gold,  mercury,  and  silver,  i.e.  from  the  metals  with 
slightly  different  solution  pressures,  but  is  easily  separated  in  potas- 
sium cyanide  solution.  This  depends  upon  the  formation  of  the  com- 
plex salt  2  K',  Pt(CN)6",  the  negative  ions  of  which  are  dissociated 
to  an  extremely  slight  extent  into  Pt""  and  6  CN'.  As  a  result  of  the 
extremely  low  concentration  of  the  ions,  the  platinum  cannot  be  pre- 
cipitated by  an  electromotive  force  which  is  sufficient  to  precipitate 
the  other  metals  the  ions  of  which  are  more  numerous.  Such  arti- 
fices are  also  often  utilized  in  technical  work,  as,  for  example,  in  the 
electrolytic  purification  of  gold.1  If  a  warm  dilute  solution  of  hydro- 
chloric acid  be  used  as  the  electrolyte,  the  gold  and  platinum  of  the 
anode  of  impure  gold  go  into  solution,  but  only  the  gold  separates 
at  the  cathode.  The  platinum  thus  becomes  accumulated  in  the 
solution  in  the  form  of  complex  ions. 

Previously,  in  the  quantitative  separation  of  the  metals,  only  the 
current-strength  was  altered.  In  a  mixture  of  zinc,  copper,  and 
silver  salts  in  acid  solution  the  silver  must  separate  first,  since  that 
process  occurs  requiring  the  least  expenditure  of  work,  which  is  also 
the  case  even  though  the  electromotive  force  be  very  high,  provided 
that  sufficient  silver  ions  are  present  at  the  electrode.  In  making 
this  statement  it  is  assumed  that  the  reaction  velocities  involved  are 
sufficiently  great.  The  current  must  be  stopped  at  the  proper 
moment,  otherwise  the  second  most  easily  separated  metal  will  be 
precipitated.  After  silver  and  copper,  hydrogen  follows.  To  pre- 
cipitate zinc  simultaneously  with  the  latter  from  an  acid  solution, 
the  current-strength  must  be  made  so  great  that  the  hydrogen  ions 
present  are  insufficient  to  convey  all  the  electricity  from  solution  to 
electrode,  and  zinc  ions  must  take  part  in  the  process.  It  is  evi- 
dently more  rational  to  choose  to  regulate  the  electromotive  force 
instead  of  the  current-strength,  whenever  possible,  for  then  it  is 
not  necessary  to  watch  over  the  electrolysis.  Until  within  the  last 
few  years  most  electrolytic  separations  were  carried  out  empirically, 
without  knowledge  of  these  theoretical  principles. 

Not  only  the  metals,  but  also  the  halogens,  can,  even  though  not 
directly,  be  separated  in  stages  by  changing  the  electromotive  force. 
For  further  information  in  regard  to  these  separations,  the  work  of 
Specketer 2  and  E.  Mtiller 3  may  be  consulted. 

•iZtschr.  Elektrochem.,  4,  402  (1898).  8  Ber.,  35,  950  (1902). 

2  Ztschr.  Electrochem,  4,  539  (1898).; 


312  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

Thus  far  in  the  discussion  of  the  phenomena  of  polarization  at> 
tention  has  been  directed  chiefly  to  insoluble  electrodes  at  which 
the  products  of  electrolysis,  especially  hydrogen  and  oxygen,  are 
separated  directly  from  the  solution.  Attention  will  now  be  given 
to  those  cases  in  which  the  product  of  electrolysis  reacts  either 
with  the  electrode  itself  or  with  some  substance  in  its  vicinity. 
A  general  idea  of  such  cases  may  be  obtained  from  the  following 
consideration :  — 

Whenever  the  evolution  of  hydrogen  or  oxygen  at  the  electrodes 
is  prevented,  depolarization  is  said  to  have  taken  place.  Depolariza- 
tion may  then  consist  of  a  reduction  at  the  anode  or  of  an  oxidation 
at  the  cathode.  When  the  electrodes  are  thus  freed  of  hydrogen 
and  oxygen,  the  electromotive  force  which  is  required  to  effect  a 
continuous  decomposition  is  less  than  that  required  before  they 
were  freed.  This  may  easily  be  shown  by  a  determination  of  the 
electrode  potentials.  This  decrease  is  due  to  the  fact  that  the  two 
gases  can  no  longer  accumulate  to  high  concentrations  at  the 
electrodes,  but  must  react  with  the  substance,  or  depolarizer,  in 
question  while  at  a  low  concentration.  The  more  energetic  the 
depolarizer  (or  mixture  of  depolarizers),  the  lower  is  the  concentra- 
tion of  the  hydrogen  and  oxygen  at  the  electrodes,  and  consequently 
the  lower  is  the  electromotive  force  required  to  carry  on  the  elec- 
trolysis. Indeed,  in  many  cases  a  spontaneous  electrolytic  process 
results,  and  the  cell,  of  itself,  produces  electrical  energy. 

The  velocity  with  which  the  hydrogen  and  oxygen  are  consumed 
naturally  plays  an  important  part.  For  example,  an  oxidizing 
agent  which,  for  small  currents,  appears  much  stronger  than 
another,  may  for  large  currents  appear  much  weaker.  The  follow- 
ing general  statement  may  be  made :  — 

An  oxidizing  or  a  reducing  agent  is  electromotively  active  in  propor- 
tion to  its  power  of  reducing  the  concentration  of  the  separated  hydro- 
gen or  oxygen. 

The  electromotive  activity  itself  is  dependent  on  the  concentration 
of  the  depolarizer  at  the  electrode,  and  therefore  indirectly  on  the 
rapidity  of  stirring,  the  velocity  of  diffusion,  and  the  current 
density  in  the  case  of  depolarizers  which  react  rapidly,  and  on  the 
specific  character  of  the  depolarizer,  catalytic  action,  and  above  all, 
on  the  temperature  in  the  case  of  depolarizers  which  react  slowly. 
These  points  have  already  been  touched  upon  in  the  discussion  of 
electro-chemical  reactions  on  page  281. 

In  the  above  consideration,  it  has  been  assumed  that  hydrogen 
and  oxygen  first  actually  separate  and  then  react  with  the  depolar- 


ELECTROLYSIS  AND  POLARIZATION  313 

izer.  In  many  cases  this  may  be  true,  but  in  others  it  certainly 
is  not  true.  For  instance,  if  zinc  is  made  an  anode  in  a  dilute  solu- 
tion of  sulfuric  acid,  it  is  very  improbable  that  the  formation  of 
zinc  ions  is  the  result  of  a  secondary  reaction  between  zinc  and  the 
separated  oxygen.  It  is  universally  assumed  that  the  zinc  ions  are 
formed  directly.  The  above  method  of  viewing  the  phenomena  of 
depolarization  is,  however,  allowable  if  it  is  only  desired  to  obtain 
a  clear  idea  of  the  formation  of  potential-difference  at  the  electrodes, 
providing,  however,  that  a  state  of  equilibrium  exists,  i.e.  that  all 
of  the  potential-differences  existing  at  the  electrode  are  equal.  (See 
also  pages  263  to  267.) 

Oxidizing  and  reducing  agents  are  extensively  used  in  electrolysis 
on  a  commercial  scale  with  more  or  less  success  in  order  to  decrease 
the  electromotive  force  required  and  thus  to  effect  a  saving  in 
electrical  energy.  Naturally  in  this  case  it  is  of  first  importance 
that  the  cost  of  the  substance  used  as  a  depolarizer  be  not  greater 
than  the  resulting  saving  in  electrical  energy.  In  his  well-planned 
process  for  the  refining  of  copper,  Hopfner  makes  use  of  a  solution 
of  sodium  and  ferric  chlorides.'  This  solution  dissolves  the  copper 
from  its  ores  in  the  cuprous  state  with  the  simultaneous  reduction 
of  the  ferric  to  ferrous  chloride.  This  copper-containing  solution  is 
sent  through  the  cathode  compartment  of  the  electrolytic  apparatus, 
where  the  copper  is  deposited.  It  is  then  sent  to  the  anode  com- 
partment, where  the  ferrous  iron  is  oxidized  to  the  original  ferric 
state.  The  solution  may  now  be  passed  through  the  same  cycle 
again.  By  the  reducing  action  of  the  ferrous  chloride  at  the  anode 
the  separation  of  chlorine  and  the  corresponding  high  electromotive 
force  is  avoided. 

Soluble  electrodes  are  used  to  attain  the  same  end,  namely,  the 
saving  of  energy. 

The  nature  of  the  reacting  substances  and  the  conditions  of  the 
experiment  determine  which  specific  reactions  will  take  place  in 
any  individual  case.  By  the  electrolysis  of  alkali  chlorides,  for 
instance,  it  is  possible  to  obtain  metal  and  chlorine,  alkali  liquor 
and  chlorine,  hypochlorite,  chlorate,  or  perchlorate.  Although  con- 
siderable success  has  already  been  attained,  this  is  still  a  field  of 
great  promise  for  experimental  research.  Space  in  this  book  is  too 
limited  for  a  consideration  of  specific  cases,  hence  the  student  is 
referred  to  the  compilation  of  F.  Forster,  "  Elektrochemie  wasserigen 
Losungen"  (1905).  Here  we  must  confine  ourselves  to  the  more 
general  points  of  view  and  their  characterization  by  citation  of 
individual  cases. 


314  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

From  one  and  the  same  substance,  it  is  possible,  especially  in 
organic  chemistry,  by  means  of  simple  oxidation  to  obtain  different 
new  substances  which,  under  comparable  circumstances,  exhibit 
different  oxidation  voltages.  If  now  this  original  substance  be 
used  as  a  reducing  agent  at  the  anode,  it  is  evident  that,  according 
to  the  magnitude  of  the  applied  anode  potential,  the  first,  second, 
third,  and  perhaps  still  higher  oxidation  stages  of  the  compound 
may  be  formed.  In  such  a  case  the  determination  of  the  decomposi- 
tion voltages  might  be  of  great  importance.  Each  decomposition 
point  indicates  the  beginning  of  a  new  reaction.  If  it  is  desired  to 
exclude  the  product  of  one  of  the  reactions,  the  electrolysis  must 
be  carried  out  with  an  electromotive  force  which  is  less  than  the 
decomposition  voltage  which  corresponds  to  this  reaction. 

In  this  manner,  Coehn 1  was  able,  by  passing  a  stream  of  acety- 
lene through  the  anode  compartment  during  the  electrolysis  of 
potassium  hydroxide  under  an  electromotive  force  which  was  be- 
tween the  first  and  the  second  decomposition  points,  to  demonstrate 
that  as  a  matter  of  fact  formic  acid  may  thus  be  formed  quantita- 
tively. Hence  in  this  case  the  entire  electrical  work  was  expended 
in  the  formation  of  formic  acid.  If  a  higher  electromotive  force  be 
employed,  a  mixture  of  substances  is  obtained,  in  which  carbon 
dioxide,  formic  acid,  and  oxygen  have  been  found. 

This  method  for  the  preparation  of  formic  acid  is  of  interest  in 
that  it  indicates  how  a  substance  may  be  prepared  without  the 
formation  of  troublesome  by-products.  Unfortunately  there  is  but 
slight  probability  that  this  process  will  become  of  value  commer- 
cially, because  with  the  limited  electromotive  force,  the  available 
current  density  is  very  small,  and  therefore  the  quantity  of  formic 
acid  formed  per  unit  of  time  is  insignificant  compared  with  the  size 
of  the  necessary  apparatus. 

Previous  to  this  work  of  Coehn,  other  similar  investigations  had 
been  carried  out,  especially  by  Haber.2  He  succeeded  in  show- 
ing that  by  reducing  nitrobenzene  at  a  given  electrode  with  the 
use  of  different  constant  electromotive  forces,  different  products  are 
obtained. 

It  is  evident  that  in  many  cases  it  is  of  importance  to  find  some 
means  of  increasing  the  potential  at  which,  for  a  given  current 
density,  oxygen  is  evolved.  With  such  a  means  at  hand,  it  might 
be  possible  that  other  oxidations,  which  are  desired,  would  take 
place  for  which  the  previous  potential  was  either  quite  too  low  or  at 

1  Ztschr.  Elektrochem.,  7,  681  (1901). 

*  Ztschr.  Elektrochem.,  4,  506  (1898)  ;  Ztschr. phys.  Chem.,  32,  193  (1900). 


ELECTROLYSIS  AND   POLARIZATION  315 

least  too  low  for  a  good  yield  of  the  desired  oxide.  Such  a  means 
has  been  found  in  the  form  of  fluorine  ions.  It  is  a  fact  that  the 
yield  of  oxidation  processes  taking  place  at  a  platinum  anode  is  con- 
siderably increased  by  the  presence  of  these  ions. 

If,  after  a  knowledge  of  the  facts  described  above  has  been  ob- 
tained, the  catalytic  influence  of  the  electrode  material  upon  the  for- 
mation of  new  substances  mentioned  on  page  275  be  recalled  to  mind, 
the  thought  is  at  once  suggested  that  the  different  potentials  existing 
at  the  electrodes  during  the  passage  of  an  electric  current  is  the 
cause  of  this  different  or  catalytic  behavior  of  the  metals.  This 
subject  is  elucidated  by  the  recently  published  work  of  Haber 
and  Kuss.1  In  this  work  they  have  shown  that  velocity  of  reduc- 
tion at  the  surfaces  of  different  metals  is  very  different  even  for  the 
same  voltage.  The  specific  influence  of  the  material  of  the  cathode 
plainly  follows  as  a  consequence  of  this  fact.  They  investigated 
especially  the  depolarizing  action  of  the  substances :  — 

Nitrobenzene,  p-Nitrophenol, 
Hypochlorite,  and  Quinhydrone, 
at  electrodes  of 

Gold,        Platinum, 
Silver,       Iron, 
and  Nickel. 

Furthermore,  they  were  able  to  confirm  the  peculiar  influence  which 
in  many  cases  the  past  treatment  of  an  electrode  exerts  upon  the 
electrolytic  process.  By  subjecting  an  electrode  to  continuous 
cathodic  polarization,  it  may  be  made  "  active,'7  i.e.  the  rapidity  of 
depolarization  at  it  may  be  increased.  This  increase  in  activity  be- 
comes evident  in  the  following  manner :  Starting  with  a  definite 
current  and  a  definite  electrode  potential,  such  that  hydrogen  is 
rapidly  evolved,  it  may  be  observed  that  the  current  increases,  the 
potential  falls,  and  the  evolution  of  hydrogen  slackens  or  ceases. 
This  active  state  is  very  unstable.  A  short  interruption  of  the  cur- 
rent is  sufficient  to  restore  the  original  state  of  the  metal. 

Summing  up,  the  conclusion  is  reached  that  the  catalytic  influence 
of  the  electrode  material,  as  well  as  the  electromotive  force,  plays  an 
important  part  in  the  electrolytic  process.  This  is  shown  also  by 
the  recent  investigation  of  Tafel  and  Naumann2  on  the  electrolytic 
reduction  of  coffeine  and  succinic  imide.  The  process  can  be 
carried  out  only  with  the  use  of  a  cathode  of  cadmium,  mercury, 

1  Ztschr.  phys.  Chem.,W,  257  (1904). 

2  Ztschr.  phys.  Chem.,  50,  713  (1905). 


316  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

or  lead.  In  the  case  of  the  latter  metal,  the  cathode  potential  must 
not  exceed  a  certain  value.  This  fact  shows  clearly  the  influence  of 
potential  on  the  process.  The  influence  of  the  electrode  material  is 
shown  by  the  fact  that  with  the  same  cathode  potential  the  reducing 
action  obtained  with  mercury  is  different  from  that  obtained  with 
lead.  The  latter  influence  also  occurs  in  the  process  mentioned  on 
page  280,  involving  Pb02. 

The  phenomena  of  the  electrolysis  of  fused  salts  are,  as  shown  by 
the  investigations  of  E.  Lorenz,1  entirely  analogous  to  those  of  aque- 
ous solutions. 

Electrolysis  with  an  Alternating  Current.2  —  If,  instead  of  a  direct 
current,  a  symmetrical  alternating  current  be  used,  it  is  at  once 
evident  that,  with  so-called  reversible  electrodes,  no  change  would  be 
detected  either  in  the  solution  of  the  electrolyte  or  at  the  electrodes. 
The  change  which  is  produced  by  the  momentary  flow  of  electricity  in 
one  direction  is  exactly  compensated  by  that  produced  by  the  next 
momentary  flow  in  the  opposite  direction.  On  the  other  hand,  if  the 
electrolysis  is  carried  out  with  such  an  arrangement  as : 

Copper  —  Acid  solution  of  sodium  sulfate  —  Copper, 

whether  or  not  copper  goes  into  the  solution  depends  upon  the  rapid- 
ity of  alternation.  If  the  current  be  but  slowly  alternated,  a  greater 
or  less  quantity  of  copper  ions  sent  into  the  solution  by  the  momen- 
tary current  in  one  direction  is  removed  from  the  immediate 
vicinity  of  the  electrode  by  diffusion  or  convection  so  that  an  insuf- 
ficient quantity  of  these  ions  are  available  at  the  electrode  for 
precipitation  by  the  next  momentary  flow  of  electricity  in  the 
opposite  direction,  then  this  deficit  is  supplied  by  hydrogen  or 
sodium  ions.  Experiments  have  shown  that  for  a  current  density 
of  0.046  ampere  per  square  centimeter  and  a  frequency  of  alterna- 
tion of  1000  per  minute  and  higher,  only  a  small  per  cent  of  copper 
goes  into  solution.  The  same  holds  for  the  system, 

Platinum  —  Sulfuric  acid  —  Platinum. 

1  See  also  Le  Blanc  and  Brode,  "The  Electrolysis  of  Fused  Sodium  and 
Potassium  Hydroxides,"  Ztschr.  Elektrochem. ,  8,  697  (1902).  More  detailed 
information  will  be  found  in  Lorenz's  "  Die  Elektrolyse  geschmolzener  Salze," 
Volumes  20,  21,  and  22  of  the  "  Monographien  fiber  angewandte  Elektro- 
chemie,"  W.  Knapp,  publisher,  Halle,  Saxony. 

2Le  Blanc  and  Schick.  Ztschr.  phys.  Chem.,  46,  213  (1903);  A.  Lob, 
Ztschr.  Elektrochem.,  12,  79  (1906).  The  reader  is  referred  also  to  the  inter- 
esting experiments  of  Drechsel,  J.  prakt.  Chem.,  29,  34,  and  38,  which  cannot 
be  considered  here. 


ELECTROLYSIS  AND  POLARIZATION  317 

In  this  case  the  quantity  of  hydrogen  and  oxygen  evolved  by  an 
alternating  current  of  high  frequency  is  practically  equal  to  zero. 

The  relations  are  quite  different  when,  for  instance,  two  copper 
electrodes  are  placed  in  a  4  normal  solution  of  potassium  cyanide. 
In  this  case,  with  an  alternating  current  of  a  frequency  of  1000  per 
minute,  the  copper  dissolves  in  the  form  of  cuprous  ions  almost 
quantitatively,  accompanied  by  the  evolution  of  an  equivalent 
quantity  of  hydrogen.  Thus  the  same  results  are  attained  as  with 
the  direct  current.  As  the  frequency  of  the  alternating  current  is 
increased,  the  quantity  of  copper  dissolved  decreases.  However, 
when  the  frequency  has  reached  38,000  reversals  per  minute,  and 
the  current  density  is  0.046  ampere  per  square  centimeter,  the  yield 
is  still  about  33  per  cent. 

The  most  probable  explanation  of  this  phenomenon  is  found  in 
the  formation  of  complex  substances.  Copper  ions  may  unite  with 
potassium  cyanide,  or  cyanide  ions,  to  form  a  complex  ion  from 
which  copper  cannot  be  separated  at  the  cathode.  If  now  the 
reversal  of  the  current  is  so  slow  that  the  copper  ions  sent  into  the 
solution  by  the  momentary  current  in  one  direction  have  sufficient 
time  to  form  the  complex  ion  with  the  cyanide  ion,  the  reverse  cur- 
rent cannot  redeposit  the  copper.  The  greater  the  frequency  of 
reversal  of  the  current,  the  greater  is  the  per  cent  of  copper  sent 
into  the  solution  which  will  be  deposited  out  again.  This  offers  a 
means  of  obtaining  an  idea  of  the  velocity  of  a  reaction  between 
ions.  Thus  the  reaction  between  copper  ions  and  potassium  cyanide 
during  the  electrolysis  of  a  4  normal  solution  of  potassium  cyanide 
between  copper  electrodes,  with  a  current  density  of  0.046,  is  prac- 
tically completed  in  y^1^  of  a  minute,  while  at  the  end  of  ^^  of  a 
minute  it  has  not  proceeded  far  enough  to  be  detected.  The  alter- 
nating current  also  throws  some  light  on  the  velocity  of  the  forma- 
tion of  difficultly  soluble  precipitates,  although  in  most  cases  the 
precipitate  formed  by  the  current  in  one  direction  is  completely 
decomposed  again  by  that  in  the  opposite  direction. 

It  will  only  be  mentioned  here  that  with  the  alternating  current 
remarkable  passivity  phenomena  occur. 

Electrolysis  without  Electrodes.  —  If  a  platinum  cathode  be  placed 
in  a  potassium  iodide  solution  and  a  platinum  anode  a  few  milli- 
meters above  the  solution,  and  an  electric  current  from  a  powerful 
electric  machine  be  sent  from  one  electrode  to  the  other,  then  iodine 
separates  at  the  boundary  surface  of  air  and  liquid.  The  quantity 
of  iodine  which  so  separates  is  that  required  by  Faraday's  law.1 

i  Klupfel,  Drud.  Ann.,  16,  674  (1905)  ;  Gubkin,  Wied.  Ann.,  32,  114  (1887). 


318  A  TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

Hence  under  these  circumstances  the  negatively  charged  iodine  ions 
give  up  their  charges  to  the  space  occupied  by  gas  or  vapor.  It  is 
possible  that  these  charges  pass  through  this  space  to  the  anode  as 
free  electrons.  If  instead  of  the  anode  the  cathode  be  placed  above 
the  solution,  the  corresponding  quantity  of  potassium  hydroxide  is 
formed  at  the  surface  of  the  liquid,  accompanied  by  the  evolution  of 
hydrogen  gas.  If,  with  this  same  arrangement  of  electrodes,  a  solu- 
tion of  a  salt  of  a  heavy  metal  be  used,  then  a  separation  of  metal 
takes  place  at  the  surface.  In  this  case  it  may  be  considered  that 
the  cathode  throws  off  free  negative  electrons,  constituting  cathode 
rays.  The  question  then  at  once  arises  as  to  the  possibility  that 
real  cathode  rays  may  have  a  reducing  action  on  the  surface  of  elec- 
trolytes. As  a  matter  of  fact,  Bose1  found  that,  under  favorable 
circumstances,  hydrogen  is  evolved  when  the  surface  of  a  hot 
saturated  alkali  solution  under  a  vacuum  is  exposed  to  the  action  of 
cathode  rays.  The  quantity  of  hydrogen  evolved  is,  however,  con- 
siderably greater  than  required  by  Faraday's  law.  Besides  the  pure 
electro-chemical  action  another  takes  place  in  this  case  which  may  be 
ascribed  to  the  kinetic  energy  of  the  particles  of  the  cathode  rays. 
It  may  be  shown  by  calculation  that  the  mechanical  energy  of  the 
cathode  rays  may,  in  the  most  favorable  case,  produce  a  much 
greater  chemical  action  than  corresponds  to  the  quantity  of  elec- 
tricity involved.  Now  even  if  by  far  the  greater  part  of  this  energy 
becomes  transformed  into  heat,  the  assumption  that  at  least  a  small 
portion  of  this  energy  is  consumed  in  the  evolution  of  detonating 
gas  is  still  plausible.  The  oxygen  gas,  which  would  be  expected 
under  this  assumption,  is  at  first  dissolved  by  the  electrolyte.  It 
may,  however,  with  continued  action  finally  be  detected.2 

In  the  case  of  the  Becquerel  rays  it  is  probable  that,  due  to  the 
higher  kinetic  energy,  the  dynamical  exceeds  the  purely  electro- 
chemicaleffect  to  a  greater  extent  than  in  the  case  of  the  cathode  rays. 

Decomposition  Voltage  and  Solubility. — That  the  voltage  at  which 
the  ions  of  a  salt  in  a  1  normal  solution  are  separated  from  the 
solution  marks  the  upper  limit  of  the  solubility  of  the  salt  has  been 
pointed  out  by  Nernst. 3  For  example,  since  the  decomposition  value 
for  iodine  ions  is 

FC  electrodes-electrolyte  =  +  0.24  VOlt, 

and  that  of  silver  ions  is 

1  Ztschr.  Wiss.  Phot.,  2,  223  (1904). 

2  It  is  also  assumed  in  the  case  of  the  formation  of  ozone  that  the  action  of 
the  cathode  rays  is  a  purely  chemical  one.    See  page  24. 

3£er.,  30,  1647  (1897). 


ELECTROLYSIS  AND  POLARIZATION  319 

^c  electrode -^-electrolyte  =  +  0.49  Volt, 

silver  iodine  could  not  exist  in  solution  to  a  concentration  of  1  nor- 
mal, because  at  such  a  concentration  it  would  become  spontaneously 
decomposed  with  a  force  of  0.25  of  a  volt.  Hence  in  order  that 
silver  iodide  should  be  capable  of  existence,  its  solubility  must 
be  exceedingly  small.  This  is  in  agreement  with  facts.  If  the 
solubility  be  calculated  for  which  the  decomposition  voltage  is  equal 
to  zero,  i.e.  at  which  the  salt  just  becomes  stable,  a  value  is  obtained 
which  is  much  larger  than  that  actually  observed.  Bodlander l  states, 
what  had  already  been  indicated  by  Luther,  that  it  is  possible  to 
calculate  exact  solubility  values  if  the  decomposition  voltage  of  the 
solid  salt  be  taken  into  consideration. 

Equilibrium  constantly  exists  between  the  saturated  (but  dilute) 
solution  of  a  practically  completely  dissociated  electrolyte  and 
the  anhydrous  solid  salt.  Then  the  work  which  must  be  done 
during  electrolysis  in  order  to  discharge  the  ions  is  equal  to  that 
which  is  required  to  break  up  the  solid  salts  into  the  same  con- 
stituents at  the  same  concentration.  Hence  we  may  consider  the 
decomposition  voltage  as  a  measure  of  the  tenacity  with  which  these 
constituents  are  held  together  in  the  solid  state. 

The  decomposition  voltage  of  the  saturated  solution  is  now,  at  17°, 

j_  j_ 

pf  =  0.0575  logfeY"  +0.0575  log  Q§V«,  (1) 

where  PC  and  vc  refer  to  the  cation,  pa  and  v0  to  the  anion,  and  P 
represents  the  equal  concentrations,  expressed  in  equivalents,  of  the 
two  ions  in  the  saturated  salt  solution. 

The  individual  decomposition  voltages  of  the  cation  ^  and  of  the 
anion  ?a  for  an  ion  concentration  of  1  normal  is  as  follows:  — 

j 
Ic  =  0.0575  log  P/ 

Ia=  0.0575  log  pa 
From  (1)  and  (2)  the  following  is  obtained:  — 

P.  =  *,  +  la  -  0.0575  lOg  P^+  ^. 

If  the  cation  and  anion  are  both  univalent, 

vc  =  va  =  l. 
lZtschr.  phys.  Chem.,  27.  55  (1898). 


320  A   TEXT-BOOK  OF  ELECTRO-CHEMISTRY 

By  substituting  this  value  in  (3),   the  following  equation  is  ob- 
tained :  — 

*=:*,  +  *,  -0.115  log  P. 

In  the  case  of  highly  dissociated  and  slightly  soluble  electrolytes, 
the  value  of  P  represents  the  solubility.  From  this  quantity,  the 
values  of  1LC  and  £a  being  known,  the  free  energy  FSQ  which  is  lib- 
erated during  the  formation  of  the  solid  substance  from  the  corre- 
sponding constituents  may  be  calculated.  Conversely,  the  quantities, 
FS,  Ec,  and  Ia  being  known,  the  value  of  P  may  be  calculated.  Of 
these  quantities,  £c  and  Za  are  easily  determined  experimentally,  and 
F,  may  in  many  cases  be  taken  as  approximately  equal  to  the 
equivalent  heat  of  formation  Q,  expressed  in  calories.  Hence 


or 


9  =  Q  X  4.189, 
x4.189=  Q 
96540  23045 


Considering  the  sources  of  error  involved,  the  calculated  values  are 
in  remarkable  agreement  with  those  actually  observed. 

Finally,  attention  is  called  to  an  empirical  rule  which  holds  in 

many  cases,  and  which,  further,  may  be  established  theoretically  by 

deductions  from  the  above  equation.    It  may  be  stated  as  follows:  — 

Tlie  solubility  of  different  salts  of  the  same  metal  (or  of  the  same 

acid)  is  the  greater,  the  greater  the  tendency  of  the  acid  radical  (or 

metal  radical)  to  pass  from  the  electrically  neutral  to  the  ionized  state. 

Thus  in  the  case  of  compounds  of  the  metals,  the  solubility  in- 

creases in  the  order,  — 

Iodine, 

Bromine, 

Chlorine, 

and  in  the  case  of  the  organic  acids,  in  the  order,— 

Silver  salt, 
Acid, 
Alkali  salt. 

Recently,  it  has  been  endeavored  to  bring  a  large  number  of  prop- 
erties into  relationship  with  the  decomposition  voltages.1 

*Abegg  and  Bodlander,  Ztschr.  anorg.  Chem.,  20,  453  (1899). 


CHAPTER  IX 

SUPPLEMENT 
STORAGE  CELLS  OR  ACCUMULATORS 

SINCE  storage  cells  are  to-day  used  to  an  extraordinary  extent  for 
many  purposes,  a  brief  presentation  of  the  chemical  processes  which 
take  place  in  them  is  here  given. 

Storage  cells  or  accumulators  are  arrangements  in  which  electrical 
energy  may  be  stored  as  chemical  energy,  whence  it  may  again 
be  obtained  at  will  in  the  form  of  electrical  energy.  Any  reversible 
cell  may  be  used  as  an  accumulator.  If  a  current  be  sent  through 
a  used  Daniell  element  in  the  direction  from  copper  to  zinc,  copper 
is  dissolved  and  zinc  precipitated  —  in  other  words,  electrical  energy 
is  stored  up  in  the  form  of  chemical  energy.  In  practice  lead 
storage  cells  are  used  almost  exclusively.1  The  electrodes  consist 
of  lead  plates  coated  with  a  specially  prepared  layer  of  lead  oxide 
or  sulfate,  and  the  electrolyte  is  20  per  cent  sulfuric  acid.  When  a 
current  is  sent  through  this  arrangement,  lead  peroxide  (or  a  cor- 
responding hydrate)  is  formed  on  that  electrode  at  which  the  positive 
electricity  enters  the  acid,  while  at  the  other  electrode  metallic  lead 
in  spongy  form  is  produced.  The  storage  cell  is  charged  after  the 
conduction  of  sufficient  electricity  through  it.  In  the  discharge 
both  the  peroxide  and  the  metallic  lead  return  to  sulfate.  The 
chemical  process  on  charging  is  then  essentially  the  change  of  lead 
sulfate  to  lead  at  one  electrode  and  to  peroxide  at  the  other,  while 
the  discharge  is  simply  the  return  of  these  substances  to  lead  sul- 
fate. The  corresponding  heat  of  reaction  is  given  by  Streintz 2  as 
follows :  — 

Pb02  +  2H2S04  aq.  +  Pb  =  2PbS04  +  2H20  +  aq.  +  87,000  cal. 
If  the  electromotive  force  of  the  storage  cell  be  calculated  from 

1  For  particulars  concerning  the  making  and  use  of  accumulators,  attention 
is  called  to  the  following  works :  — 

Heim,  "  Die  Akkumulatoren"  (Oskar  Leiner,  Leipzig). 

Elbs,  "  Die  Akkumulatoren"  (Johann  Ambrosius  Earth,  Leipzig). 

2  Wiener  Monatshefte  f.  Chemie,  15,285  (1894). 

Y  321 


322  A  TEXT-BOOK  OF   ELECTRO-CHEMISTRY 

the  known  heat  of  reaction,  assuming  complete  transformation  into 
electrical  energy,  1.885  volt  is  obtained.  This  agrees  very  well  with 
the  experimentally  determined  value  for  dilute  sulfuric  acid.  From 
this  agreement  it  also  follows  that  the  electromotive  force  of  the 
storage  cell  is  nearly  independent  of  the  temperature  (page  173),  and 
this  has  also  been  demonstrated  by  Streintz.  If  this  shows  that 
it  is  probable,  the  work  of  Dolezalek1  removes  all  doubt,  that  the 
process  takes  place  in  the  manner  indicated.  Dolezalek  showed 
that  the  entire  behavior  of  the  storage  cell  is  in  agreement  with  the 
reaction  equation.  He  investigated  especially  the  relation  between 
the  electromotive  force  and  the  concentration  of  the  acid,  and  estab- 
lished the  fact  that  the  values  calculated  from  thermodynamical 
considerations  agree  finely  with  the  values  found  by  experiment, 
and  that  therefore  (for  small  current  densities)  the  storage  cell  is 
reversible.  These  results  are  in  complete  agreement  with  the  theory 
advanced  by  Le  Blanc 2  by  which  the  processes  taking  place  in  the 
storage  cell  were,  for  the  first  time,  explained  with  the  aid  of  the 
ionic  theory. 

When  the  storage  cell  is  charged  and  ready  for  use,  the  positive 
electrode  is  coated  with  lead  peroxide  and  the  negative  with  spongy 
lead.  Between  the  two  electrodes  is  sulfuric  acid.  It  may  be 
assumed  that  lead  peroxide  in  contact  with  water  forms  tetravalent 
lead  ions  together  with  the  corresponding  hydroxyl  ions,  and  that 
while  the  cell  is  in  action  the  tetravalent  ions  are  transformed  into 
divalent  lead  ions.  This  process  is  the  chief  source  of  the  electromotive 
force  of  the  storage  cell.  The  tetravalent  ions  which  disappear  are 
constantly  replaced  from  the  solid  lead  peroxide,  and  the  bivalent 
ions  which  are  formed  do  not  remain  in  the  solution,  but  since  lead 
sulfate  is  difficultly  soluble,  i.e.  since  the  product  of  the  concentra- 
tions of  the  divalent  lead  ions  and  the  sulfate  ions  is  a  small  value, 
they  combine  with  the  sulfate  ions  in  the  solution,  forming  solid 
lead  sulfate. 

At  the  negative  pole  metallic  lead  changes  into  bivalent  ions,  a 
process  taking  place  without  producing  any  considerable  potential 
difference.  Here  also  insoluble  lead  sulfate  is  formed  from  the 
Pb"  and  S04". 

The  ionic  theory  not  only  renders  clear  the  changes  of  peroxide 
and  metallic  lead  into  sulfate,  but  also  explains  the  gradual 
diminution  of  the  electromotive  force  of  the  cell  in  action.  While 

1  Wied.   Ann.,   65,  894   (1898),  and   «  Theorie  des  Bleiakkumulators, "  W. 
Knapp,  Halle,  Saxony  (1901). 

2  First  edition  of  this  book,  page  223  (1895). 


SUPPLEMENT  323 

the  magnitude  of  the  potential-difference  at  the  positive  electrode 
depends  upon  the  concentration  of  the  quadrivalent  and  bivalent 
lead  ions  (see  page  250),  that  of  the  potential-difference  at  the 
negative  electrode  depends  upon  the  concentration  of  divalent  lead 
ions  in  contact  with  an  excess  of  metallic  lead.  The  concentration 
of  the  quadrivalent  ions  decreases  with  time,  and  that  of  the  bivalent 
increases,  as  may  be  seen  from  the  following :  At  the  peroxide 
electrode  there  is  a  saturated  solution  of  this  compound — that  is, 
the  product  of  the  concentration  of  Pb::  and  the  fourth  power1  of  the 
concentration  of  the  OH'  ions  is  here  constant.  On  the  other  handy 
there  must  be  definite  relations  between  these  ions  and  those  of  the 
sulfuric  acid.  The  product  of  the  concentration  of  the  H  and  OH 
ions  in  the  solution  must  have  a  constant  value  equal  to  that  for 
water.  It  has  been  seen,  in  the  first  place,  that  during  the  discharge 
of  the  cell,  lead  sulfate  is  formed  at  the  peroxide  electrode,  and  in 
the  second,  that  newly  formed  OH  ions  produced  by  the  peroxide 
cannot  exist  as  such,  but  must  combine  with  the  H  ions  of  the  acid 
to  form  undissociated  water.  There  is  thus  a  continual  removal  of 
H  and  S04  ions  taking  place.  The  removal  of  the  former  allows  of 
an  increase  in  the  concentration  of  the  OH  ions,  and  therefore  causes 
a  reduction  in  that  of  the  quadrivalent  lead  ions.  The  removal  of 
S04  ions  permits  an  increase  in  the  concentration  of  the  Pb"  ions, 
since  the  solution  is  saturated  with  lead  sulfate.  This  latter 
process  also  takes  place  at  the  negative  electrode.  When  the  supply 
of  peroxide  is  exhausted,  the  electromotive  force  falls  very  rapidly  to 
an  exceedingly  low  value. 

After  the  cell  has  been  discharged,  there  is  lead  sulfate  on  both 
electrodes,  consequently  bivalent  lead  ions  are  present.  The  process 
of  charging  consists  simply  in  the  change  of  bivalent  lead  ions  to 
quadrivalent  at  the  electrode  at  which  the  positive  electricity  enters 
the  solution,  and  to  metallic  lead  at  the  other  electrode.  The  Pb" 
ions  used  are  replaced  from  the  solid  lead  sulfate.  The  Pb"  ions  and 
the  OH'  ions  present,  having  reached  that  concentration  in  the  solu- 
tion determined  by  the  dissociation  constant  for  peroxide  of  lead, 
combine  to  form  this  oxide  (or  a  hydrate).  Thus  the  lead  sulfate 
at  one  electrode  gradually  changes  into  peroxide,  and  into  metallic 
lead  at  the  other.  The  opposing  electromotive  force  of  the  cell 
increases  during  the  charging,  because  the  processes  described  as 
taking  place  during  discharge  are  reversed.  The  concentration  of 
the  bivalent  lead  ions  at  both  electrodes  diminishes  with  time,  while 
that  of  the  S04"  ions  is  continually  increasing.  The  concentration  of 
1  Because  four  OH  ions  correspond  to  one  of  the  lead  ions. 


324  A  TEXT-BOOK   OF  ELECTRO-CHEMISTRY 

the  Pb::  ions  increases  with  the  increase  of  H  ions  formed  with  equiv- 
alent quantities  of  OH  ions  from  the  undissociated  water.  The 
OH'  ions  continually  combine  with  the  Pb"  to  form  peroxide,  and 
their  concentration  must  diminish  as  that  of  the  hydrogen  ions  in- 
creases. The  lower  the  concentration  of  the  OH  ions  the  greater  is 
that  of  the  Pb"  ions.  If  no  more  bivalent  lead  ions  are  present, 
hydrogen  ions  separate  at  one  electrode  and  hydroxyl  ions  at  the 
other.  Thus  the  rapid  generation  of  hydrogen  and  oxygen  at  the 
electrodes  in  charging  shows  that  the  accumulator  is  over-charged. 
In  order  to  cause  a  considerable  generation  of  hydrogen  and  oxygen 
in  the  cell  a  somewhat  higher  electromotive  force  is  required  than  is 
necessary  to  charge  it,  since  the  separating  gases  can  accumulate  to 
high  concentrations  in  the  electrodes,  or,  in  other  words,  since  the 
electrodes  possess  a  considerable  over-voltage.  When  platinum  elec- 
trodes are  used  in  sulfuric  acid,  an  electromotive  force  of  two  volts  is 
sufficient  to  produce  a  rapid  evolution  of  gas.  If  this  was  also  the 
case  in  the  lead  cell,  the  latter  could  be  charged  only  with  a  great 
loss  of  energy. 

The  above  theory  of  the  processes  which  take  place  in  the  storage 
cell  has  received  considerable  support  from  the  recent  work  of  Elbs 
and  Eixon,1  which  has  established  the  fact  that  acid  which  has  been 
in  use  in  such  cells  contains  comparatively  large  quantities  (as  much 
as  0.17  of  a  gram  of  Pb(S04)2  per  liter)  of  tetravalent  lead,  and  hence 
of  tetravalent  lead  ions.  By  a  special  experiment  it  was  proven  that 
the  equilibrium  corresponding  to  the  reaction  equation,  — 


Pb(S04)2  +  2H2O^TPb02  +  2  H2S04, 

is  attained  in  about  five  hours,  when  a  mixture  of  freshly  precipitated 
lead  peroxide  and  sulfuric  acid  is  continuously  stirred.  The  presence 
of  the  above-mentioned  considerable  quantity  of  tetravalent  lead  in 
the  acid  furnishes  a  plausible  explanation  of  the  spontaneous  dis- 
charge of  accumulators.  The  tetravalent  lead  migrates  from  the 
peroxide  electrode,  where  it  is  formed,  to  the  spongy  lead  electrode, 
where  it  is  reduced  to  the  bivalent  state. 

It  must  not,  however,  be  supposed  that  only  the  assumed  process, 
especially  the  formation  of  tetra-  or  bivalent  lead  ions  at  the  anode, 
takes  place.  According  to  Liebenow,  it  is  possible  that  the  ion 
Pb02"  is  present,  and  is  transformed  reversibly  into  ordinary  PbO2. 
In  describing  states  of  equilibrium,  as,  for  example,  in  measurements 
of  potential,  it  makes  no  difference  to  which  of  the  reactions  of  the 

1  Ztschr.  Elektrochem.,  9,  267  (1903). 


SUPPLEMENT 


325 


equilibrium  the  source  of  the  electromotive  force  is  ascribed.  In 
describing  the  process  of  electrolysis,  however,  it  is  absolutely  nec- 
essary to  emphasize  the  reaction  in  which  the  greatest  quantities 
are  involved.  Which  of  the  reactions  this  is  depends  upon  the 
respective  velocities  of  reaction,  and  must  be  determined  for  indi- 
vidual cases.  In  the  case  in  question  it  appears  more  in  accord  with 
facts  to  give  prominence  to  Pb::,  and  not  to  PbO2"  ions,  because  the 
concentration  of  the  latter  is  insignificant  in  comparison  with  that 
of  the  former.  (See  also  page  307.) 

Of  the  storage  cells  using  metals  other  than  lead,  the  Junger-Edison 
accumulator  is  the  most  interesting.1  When  charged  it  consists  of 
the  combination, 

Fe  —  KOH  —  Ni2O3,  aq. 

During  the  charging  and  the  discharging  of  the  cell,  the  following 
processes  take  place :  — 

Fe  +  2  Ni(OH)  5zFe(OH)  +  2  Ni(OH)2,  or 
Fe  +  Ni203,  n  HzO  ±  r  H2O^FeO,  m  H20  +  (NiO),,  p  H20. 

Hence  in  this  cell  water  plays  the  greatest  part  in  the  reaction. 
For  this  reason,  but  little  alkali  is  required  in  the  cell.  This  is  in 
contrast  to  the  lead  accumulator,  in  which  much  sulf  uric  acid  is  used. 
The  normal  initial  voltage  is  1.36  volts.  The  value  of  this  storage 
cell  in  practical  service  remains  to  be  determined. 


ENERGY-EQUIVALENTS  (see  page  18) 


ERGS 

JOULES 

CALORIES  * 

KILOGRAM- 

METERS 

LITER- 
ATMOSPHERES 

KILOWATT- 
HOURS 

HORSE. 

POWER 

1 

10-7 

2.387x10-8 

1.020x10-8 

9.872xlO-i<> 

2.778x10-" 

3.776x10-" 

10' 

1 

0.2387 

0.1020 

9.872xlO-» 

2.778x10-' 

3.776x10-' 

4.189x10* 

4.189 

1 

0.4272 

4.135x10-2 

1.164x10-" 

1.582xlO-« 

9.806xl07 

9.806 

2.341 

1 

9.861x10- 

2.724xlO-« 

3.703xlO-« 

1.013xlO» 

101.8 

24.18 

10.33 

1 

2.814xlO-» 

8.825xlO-» 

3.600  xlO" 

3.600xlO« 

8.593x10' 

8.672x10" 

3.553x10* 

1 

1.359 

2.  649x10" 

2.649xlO« 

6.325x10* 

2.T02xlOB 

2.616x10* 

0.7360 

1 

1  Elbs,  Ztschr.  Elektrochem. ,  11,  734  (1905)  ;  Grafenberg,  Ztschr.  Elektro- 
chem.,  11,  736  (1905)  ;  Zedner,  Ztschr.  Elektrochem.,  11,  809  (1905)  ;  Forster, 
Ztschr.  Elektrochem.,  11,  948  (1905).  See  also  the  discussion  following  the  above 
papers. 

2  The  calorie  (15°  gm-cal.)  here  is  that  recommended  by  the  International 
Congress  for  Applied  Chemistry  at  Berlin,  namely,  equal  to  4.189x  107  ergs. 


326 


A  TEXT-BOOK  OF   ELECTRO-CHEMISTRY 


ELECTRO-CHEMICAL  CONSTANTS  (see  page  43) 

Mec  represents  electro-chemical  equivalents,  or  the  quantity  or  mass 
of  substance  in  milligrams  which  is  separated  by  one  ampere-second, 
and  3600  •  Mec  represents  the  quantity  or  mass  in  grams  of  various 
anions  and  cations  which  is  separated  by  one  ampere-hour  of  elec- 
tricity (=  0.0373  equiv.). 


CATIONS 

EQTTIV. 

-. 

3600  •  Mec 

ANIONS 

EQUIV. 

«. 

8600  •  Mec 

|Ai 

9.03 

0.09354 

0.3367 

Br 

79.96 

0.8282 

2.982 

i  Sb 

40.07 

0.4151 

1.494 

Br08 

127.96 

1.325 

4.772 

i  As 

26. 

0.2590 

0.9322 

Cl 

35.45 

0.3672 

1.322 

£Ba 

68.7 

0.7116 

2.562 

C108 

83.45 

0.8644 

3.112 

\  Pb 

103.45 

1.072 

3.858 

CHO2 

45.01 

0.4662 

1.678 

*Cd 

56.2 

0.5821 

2.096 

C2H302 

59.02 

0.6114 

2.201 

iCa 

20.05 

0.2077 

0.7477 

CN 

26.04 

0.2697 

0.9710 

T  Cr 

17.37 

0.1799 

0.6477 

•j  CO3 

30.00 

0.3108 

1.119 

I  Fe 

27.95 

0.2895 

1.042 

•g  C2O4 

44.00 

0.4558 

1.641 

£Fe 

18.63 

0.1930 

0.6947 

\  Cr04 

58.05 

0.6013 

2.165 

1  Au 

65.73 

0.6808 

2.451 

Fl 

19. 

0.1968 

0.7085 

K 

39.15 

0.4055 

1.460 

I 

126.97 

1.315 

4.735 

\  Co 

29.5 

0.3056 

1.100 

I03 

174.85 

1.811 

6.520 

Cu 

63.6 

0.6588 

2.372 

N03 

62.04 

0.6426 

2.313 

iCu 

31.8 

0.3294 

1.186 

to 

8. 

0.08287 

0.2983 

Li 

7.03 

0.07282 

0.2621 

OH 

17.01 

0.1762 

0.6343 

i  Mg 

12.18 

0.1262 

0.4542 

\  Si03 

38.20 

0.3957 

1.424 

i  jfln 

27.5 

0.2849 

1.025 

\  s 

16.03 

0.1660 

0.5978 

Na 

23.05 

0.2388  . 

0.8595 

£Se 

39.6 

0.4102 

1.477 

\  Ni 

29.35 

0.3040 

1.094 

\  so* 

48.03 

0.4975 

1.791 

Hg 

200.0 

2.072 

7.458 

£Te 

63.8 

0.6609 

2.379 

Ag 

107.93 

1.118 

4.025 

i  Sr 

43.8 

0.4537 

1.633 

iTe 

31.9 

0.3304 

1.190 

Tl 

204.1 

0.2114 

0.7611 

H 

1.008 

0.01044 

0.03759 

\  Zn 

32.7 

0.3387 

1.219 

£  Sn 

69.5 

0.6163 

2.219 

iSn 

29.75 

0.3082 

1.109 

APPENDIX 


NOTATION 

SINCE  there  is  no  recognized  system  of  notation  in  electro- 
chemistry, it  has  been  endeavored  in  this  translation  to  devise  and 
introduce  a  system  of  notation  which  shall  be  simple,  and  shall  avoid 
the  difficulty  and  confusion  often  caused  by  the  use  of  complicated 
or  unsystematized  notation.  While  the  system  given  here  is 
original  as  a  whole,  yet  in  nearly  every  case  the  individual  symbols 
have  been  used  with  a  similar  meaning  in  some  other  work  on 
chemical  or  electrical  science.  Hence  it  will  scarcely  be  necessary 
for  any  one  at  all  familiar  with  chemical  or  electrical  literature  to 
study  the  system.  It  is  also  believed  that  students  and  general 
readers  of  the  book  will  experience  no  difficulty  or  confusion  in 
keeping  the  notation  in  mind. 

In  devising  the  system,  each  class  of  properties,  quantities,  etc., 
has  been  represented  by  a  Roman  letter  which,  while  avoiding 
ambiguity,  readily  suggests  the  class  in  question.  Thus  concentra- 
tion has  been  represented  by  the  letter  (7,  and  dilution  by  the  letter 
D.  Whenever  the  names  of  two  or  more  classes  have  the  same 
initial  letter,  the  use  of  a  single  character  to  represent  them  has 
been  avoided  by  the  use  of  small  letters,  small  capitals,  and  large 
capitals,  or  of  different  letters  which  may  be  substituted  for  the 
initial  letters  without  materially  affecting  the  sound  of  the  class 
names.  This  may  be  illustrated  by  the  following  examples:  — 

Concentration  (of  a  gas)  =  c 

Current  (electric)  =  c 

Concentration  (of  a  solid  or  liquid)  =  C 
Conductance  (electrical)  =  K 

Constant  =  K 

The  class  notation  adopted  is  given  in  the  following  table:  — 
A      .     .     .     ACIDITY. 
B      .    .    *    BASICITY. 
c       ...    ELECTRIC  CURRENT. 

327 


328  APPENDIX 


B-) 
(4) 


(7  ...  CONCENTRATION. 

d  ...  DlFFERENTAL. 

D  ...  DIFFUSION. 

D  .    .     .  DILUTION. 

E  .     .     .  ENERGY. 

F  .     .     .  FORCE.     (Factor  or  function  =  /.) 

H  .     .     .  HEAT  OR  HEAT  CAPACITY. 

K  ...  ELECTRICAL  CONDUCTANCE.     (=-•] 

K  .     .    .  CONSTANT.     (Capacity  =  fc). 

/  ...  LENGTH,  HEIGHT,  DISTANCE. 

M  .     .    .  MASS  OR  WEIGHT. 

n  ...  NUMBER.     (Normal  concentration  =  N.) 

P  .    .    .  PRESSURE. 

Q  .    .    .  QUANTITY. 

R  ELECTRICAL  KESISTANCE. 


H-) 

(-5) 


JR     .    .    .     GAS  AND  SOLUTE  CONSTANT. 

s  ...  SURFACE  OR  CROSS  SECTION. 

S  ...  SOLUBILITY. 

T  ...  TIME. 

T  .     .     .  TEMPERATURE. 

U  .     .     .  VELOCITY. 

v  ...  VALENCE  OR  NUMBER  OF  CHARGES  ON  AN  ION. 

V  .     .     .  VOLUME. 

W  .     .     .  WORK. 

ai  ...  FRACTIONAL  PART.     DEGREE  OF  DISSOCIATION. 

It  should  be  noted  that  electrical  quantities  are  in  general  repre- 
sented by  small  capitals. 

The  whole  system  is  based  on  the  class  notation  just  given,  the 
individual  members  of  a  class  being  represented  by  the  class  letter 
with  distinguishing  sub  letters.  This  is  illustrated  by  the  following 
example :  — 

Concentration  (general)  =  C. 

Concentration  in  grams  per  liter          =  Cg. 

Concentration  in  equivalents  per  liter  =  Ce  or  Cn. 

Concentration  in  niols  per  liter  =  Cm. 


APPENDIX  329 

In  the  case  of  conductance,  a  different  rule  has  been  followed. 
The  various  kinds  of  conductances  have  been  distinguished  as 
f ollows :  —  Conductance  (general)  =  K. 

Specific  Conductance       =  K. 

Equivalent  Conductance  =  K. 

Symbols  have  been  distinguished  by  an  underline  also  in  the 
following  cases :  — 

Quantity  of  Electricity  (general)  =Q. 

Quantity  of  Electricity,  96540  coulombs  =  Q. 
Quantity  of  Heat  (general)  =  Q. 

Quantity  of  Heat,  1  calorie  =  Q. 

Electromotive  Force  (general)  =  F. 

Single  Potential-difference  =  F. 

The  complete  system  of  notation  is  given  in  alphabetical  order 
in  the  following  table:  — 

a  ...  Acceleration. 

A  .     .    .  Acidity. 

B  .    .    .  Basicity. 

c  .    .    .  Concentration  of  a  gas.     (=-.] 

\  <u 

cg     Grams  per  liter. 

cm     Mols  per  liter. 

ce     Equivalents  per  liter. 

c      .     .     .    Electric  current  or  current-strength.     (=-.) 

\     */ 

C    .    .    .    Concentration  of  a  solute.     j=—.j 

Cg     Grams  per  liter. 

Ce     Equivalents  per  liter. 

Cm     Mols  per  liter. 

d  Differential. 


d     .     .     .    Dilution  of  a  gas.    {=-.) 

V     c  ) 


Dilution  of  a  solute.     I  =  — . 


Dg     Volume  in  liters  containing  one  gram. 

De     Volume  in  liters  containing  one  equivalent. 

Dm    Volume  in  liters  containing  one  mol. 


330  APPENDIX 

D     .    .    .    Diffusion. 

DTO     Coefficient. 
E    .    .    .    Energy. 

Ee  or  E    Electrical  energy. 

En    External  energy. 

Ef     Free  energy. 

Eh     Heat  energy. 

Ein    Internal  energy. 

Em    Mechanical  energy. 

Ev     Volume  energy. 

/     .    .    .    Factor  (or  function). 

F    .    .    .    Force. 

Fe  or  F     Electromotive  force. 

FC    Referred  to  the  standard  calomel  cell. 

FA    Eeferred  to  the  standard  hydrogen  cell. 

F      Single  potential-difference. 

FC     Single  potential  referred  to  calomel  cell. 

FA    Single  potential  referred  to  hydrogen  cell. 

FO  or  (EP)    Single  potential  at  unit  concentration. 
Fm    Mechanical  force  (pressure). 

H  .    .    .    Hea,t  or  heat  capacity. 

He    Electrical  heat  effect  (Joule's  heat  effect). 
Hr    Heat  of  reaction. 
Hd    Heat  of  dissociation. 
Hn    Heat  of  neutralization. 

.    Electrical  capacity. 
.    Electrical  conductance. 

S    Specific  conductance  or  conductivity. 

g    Equivalent  conductance. 

K  .    .    .    Constant. 

Kc  Cell  constant. 

Kd  Dissociation  constant. 

Ke  Equilibrium  constant. 

KD  Dielectric  constant. 

Ks  Solubility  constant. 

Kv  Velocity  constant. 

.     Length,  height,  or  distance. 

.    Mass  or  weight  of  a  gas. 

mat    Atomic  mass  in  grams  (gram-atom  or  atom). 
mm    Molecular  mass  in  grams  (gram-mol  or  mol). 


APPENDIX  331 

M  .     .    .    Mass  or  weight  of  a  solute,  liquid  or  solid. 

Mat    Atomic  mass  in  grams  (gram-atom  or  atom). 

Meq    Equivalent  mass  in  grams  (gram-equivalent  or 
equivalent). 

Mi      Ion  mass  in  grams  (gram-ion  or  ion). 

Mm    Molecular  mass  in  grams  (gram-mol  or  mol). 
n     .    .    .    Number. 

na    Transference  number  for  anions  (  =  1  —  nc). 

nc    Transference  number  for  cations  (  =  1  —  na). 

7it-     Number  of  ions  formed  from  one  molecule  of  an 
electrolyte. 

nm    Number  of  molecules  formed  from  one  molecule. 

N   .     .    .    Normal  concentration. 

p     .     .     .     Pressure  of  a  gas. 

p     .    .    .    Electrolytic  solution  pressure. 

P    .     .    .    Pressure  of  a  solute,  i.e.  solute  or  osmotic  pressure. 

q     .     .     .     Quantity  of  magnetism. 

Q     .    .     .    Quantity  of  electricity. 

Q    Electro-chemical  unit  of  quantity  of  electricity,  i.e. 

96540  coulombs. 
Q    .    .    .    Quantity  of  heat. 

Q    Quantity  of  heat  required  to  raise  the  temperature 

of  one  gram  of  water  one  degree,  i.e.  1  calorie. 
r     .    .    .    Internal  electrical  resistance  of  cells. 
B     .     .    .    Electrical  resistance.    External  resistance  of  a  circuit 

R    .    .    .    Gas  or  solute  constant.     (=^.j 

\     nT  J 
s     .    .    .     Surface  or  cross  section. 

S     .     .    .     Solubility. 

t      .    .    .    Temperature,  centigrade  scale. 

T     .    .     .    Time. 

Td     Time  in  days. 

TA     Time  in  hours. 

Tm     Time  in  minutes. 

T,     Time  in  seconds. 
T    .    •     .    Temperature,  absolute  scale. 
U     .    .     .     Migration  velocity  of  ions. 

ua    Of  anions. 

uc    Of  cations. 


332  APPENDIX 

Ut  -     •     .  Velocity  of  solution. 

Ur  .     .     .  Velocity  of  reaction. 

v  .    .     .  Volume  of  a  gas. 

v  ...  Valence.     Number  of  electrical  charges  on  an  ion. 

F  .     .     .  Volume  of  a  liquid  or  solid. 

W   .    .    .     Work. 

Wm  Mechanical. 

We  Electrical. 

WM  Osmotic. 

«...    Fractional  part.     Degree  of  dissociation. 

A     .    •         Fractional  change. 

A,    Due  to  temperature  change  of  one  degree. 


AUTHOR  INDEX 


Abegg,  122,  123,  206,  247,  250,  255,  266, 

267,  320. 
Adolph,  82. 

Arrhenius,  49,  52,  58,  59,  89,  94,  135,  136. 
Avogadro,  52. 

Bancroft,  255. 

Basset,  76. 

Behrend,  205,  217. 

Bender,  136. 

Bernfeld,  196. 

Berzelius,  40,  41,  44,  46. 

Billitzer,  159,  239,  242. 

Biltz,  143, 158. 

Bindschedler,  276. 

Blake,  123. 

Bodlander,  128,  206,  319,  320. 

Borchers,  20,  21. 

Bose,  154,  305,  308,  318. 

Bottger,  93,  217. 

Boyle,  52. 

Brand,  307. 

Braun,  51,  159,  165. 

Bredig,  79,  116,  117, 128,  226,  269,  299. 

Brislee,  309. 

Erode,  23,  40,  316. 

Brunner,  181,  281. 

Bugarsky,  173,  222. 

Cantoni,  82. 

Carlisle,  36. 

Carrier,  82. 

Caspari,  298,  299. 

Castner,  39. 

Centnerszwer,  142. 

Chilesotti,  255. 

Clausius,  48,  49,  91, 166. 

Coehn,  159,  291,  298,  299,  305,  314. 

Cohen,  226,  271. 

Coolidge,  132. 

Czapski,  173. 

Daniell,  46. 
Danneel,  38,  93,  206. 
Danneuberg,  291,  298. 
Davy,  38,  39,  40, 123. 
Des  Coudres,  180, 19L 
Dolezalek,  322. 
Drechsel,  316. 
Dufay,  31. 


Elbs,  321,  324,  325. 
Ermann,  37,  154, 156. 
Euler,  135,  150. 

Fanjung,  136. 
Faraday,  42,  43,  44. 
Fausti,  81. 

Forster,  279,  301,  313,  325. 
Franklin,  31. 
Frazer,  56. 
Fraunberger,  247. 
Fredenhagen,  254,  263. 
Freudenberg,  310. 
Fritsch,  154. 

Galvani,  32,  33. 
Gay-Lussac,  52. 
Gibbs,  51,  165. 
Gilbert,  31. 
Glaser,  F.,  82,  277. 
Glaser,  L.,  294,  301,  305. 
Gockel,  173. 
Goodwin,  93,  204,  212. 
Gordon,  201. 
Graetz,  153. 
Grafenberg,  307,  325. 
Grotthus,  45,  47,  49. 
Gubkin,  317. 

Haagn,  104. 

Haber,  186,  206,  252,  283, 294, 299, 307, 314, 

315. 
Haskell,  93. 
Heil,  230. 
Heilbrun,  81. 
Heira,  321. 
Heimrod,  43. 
Helmholtz,  26,  51,  158,  165,  224,  234,  239, 

240,242. 
He'roult,  21. 
Herschkowitz,  186. 
Heydweiller,  129. 
Hisinger,  40. 

Hittorf,  47, 49,  63,71,75,  76,  79  80,  91,  278. 
Hofer,  307. 

Hoff ,  van't,  52,  56,  95,  96,  226,  269. 
Holborn,  83. 
Hollemann,  140. 
Hopfner,  313. 
Hulett,  163. 


334 


AUTHOR  INDEX 


Ihle,  279. 
Inglis,  307. 
Isenburg,  276. 

Jager,  162,  163. 
Jahn,  83,  173,  249. 
Jones,  76,  131. 
Just,  156,  276. 

Kahlenberg,  142,  249. 

Kanolt,  79. 

Kettenbeil,  82. 

Kiliani,  310. 

Kliipfel,  317. 

Knupffer,  269. 

Kohlrausch,  47,  49,  76,  83,  88,  89,  92,  93, 

99,  119,  128, 129,  130,  131, 140,  146,  153, 

210. 

Konig,  240. 
Konigsberger,  292. 
Kriiger,  178,  242. 
Kiister,  140. 

Labendzinski,  247,  250. 

Lash  Miller,  275. 

Le  Blanc,  40,  82,  83,  180,  194,  267, 276,  277, 

285, 287,  289,  291,  293,  309,  316,  322. 
Lehmann,  O.,  24. 
Levi,  277. 
Lewis,  247,  272. 
Liebenow,  324. 
Lippmann,  234. 
Lobry  de  Bruyn,  79. 
Lodge,  122,  123. 
Loeb,  A.,  316. 
Loeb,  M.,  73. 
Lorenz,  81, 154,  316. 
Luckow,  276. 
Luther,  181,  245,  247,  255,  267,  273,  278, 

280,  307,  309,  319. 

Maitland,  255. 

Masson,  122. 

Merriam,  297. 

Meyer,  185. 

Moest,  307. 

Morgan,  79. 

Morse,  56. 

Moser,  201. 

Miiller,  E.,  280,  301,  311. 

Miiller,  W.,  277,  292. 

Muthmann,  247. 

Naumann,  315. 

Nernst,  73,  76,  78,  104,  145,  146,  147,  154, 

166,  173,  175,  181,  200,  204,  209,  218, 219, 

221, 226, 228, 239,  241,  243,  281,  297,  305, 

318. 

Neumann,  249. 
Nicholson,  36. 
Noyes,  A.  A.,  75,  78,  83,  94,  114,  125,  132, 

139,  281. 


Oberbeck,  292. 

Ogg,  186. 

Ohm,  8,  155. 

Osaka,  299. 

Ostwald,    47,    54,    89,    94,    95,    99,    101, 

108,  114,   126,  175,  185,  205,  i212,  239, 

261. 

Palaz,  146. 
Palmaer,.241. 
Paschen,239. 
Peters,  254. 
Pfeffer,  54. 
Piguet,  301. 
Planck,  56,  124. 
Poincare,  153. 

Quincke,  157. 

Ramsay,  R.  R.,  193. 
Ramsay,  W.,  148. 
Raoult,  56. 
Reinders,  186. 
Reuss,  157. 
Richards,  43. 
Riesenfeld,  76. 
Ritter,  34. 
Rixon,  324. 
Rose,  140. 

Rothmund,  238,  272. 
Russ,  283,  315. 

Sack,  299. 

Sackur,  277. 

Sammet,  246,  247,  255, 273. 

Schaum,  254. 

Schick,  316. 

Schiller,  180. 

Schilow,  278. 

Scudder,  107. 

Seebeck,  228. 

Shields,  148. 

Shukoff,  267. 

Simon,  38. 

Smale,  294. 

Smith,  114. 

Seller,  280. 

Specketer,  311. 

Spencer,  255. 

Steele,  122,  123. 

Stefan,  281. 

Steiner,  82. 

Storbeck,  128. 

Streintz,  321,  322. 

Tafel,  280,  300,  301,  .315. 
Thales,  31. 
Thatcher,  266. 
Thomson,  145,  165. 
Tower,  83. 


AUTHOR  INDEX 


335 


Voege,  279. 

Volta,  33,  34,  35,  36,  49,  50,  221,  231. 

Walden,  76,  142,  143,  147, 151,  285. 
Walker,  79,  116. 
Warburg,  24,  154,  234. 
Wegscheider,  116,  119. 
Weigert,  309. 
West,  131. 


Whetham,  122,  123. 
Whitney,  123,  281. 
Wiedemann,  157. 
Wilke,  31. 
Wilsmore,  243,  247. 
Wohlwill,  311. 
Wulf,  297. 

Zedner,  325. 


SUBJECT  INDEX 


Accumulators,  321. 

Acids,  bases,  and  salts,  abnormality  of,  57. 

Activity  coefficient,  58. 

Additive  properties,  90. 

Additivity  of  electrical  conductance,  89. 

Affinity  constant,  definition,  95. 

Affinity  constant,  relation    to   chemical 

constitution,  116. 
Affinity  of  acids  and  bases,  95. 
Alternating  current,  electrolysis  by  means 

of,  316. 

Ampere,  definition,  8. 
Amphoteric  electrolytes,  79. 
Analysis  by  means  of  conductance  meas- 

urements, 136. 
Application  of  migration  velocity  to  com- 

mercial processes,  81. 
Avogadro's  principle,  generalized,  52. 

Basicity  law  (K1024  —  K32)  ,  126. 
Bell  process  for  the  manufacture  of  caus- 
tic soda,  82. 

Cadmium,  or  Weston,  standard  cell,  163. 

Capacity,  electrical,  24. 

Catalytic  influence  on  the  electromotive 

force,  275. 
Cell  constant,  103. 
Chemical  analysis  by  electrical  conduct- 

ance, 136. 
Chemical  and  electrical  energy,  relation, 

49,  165. 

Chemical  cells,  231. 

Chemical  compounds  as  electrodes,  188. 
Chemical  constitution,  relation  to  disso- 

ciation constants,  111,  116. 
Chemical  equilibrium  and  electromotive 

force,  267. 
Chromic  acid,  regeneration  by  electrolysis, 

83. 

Clark  standard  cell,  163. 
Clausius  theory  of  electrolysis,  47. 
Colloidal  metal-solutions,  preparation,  24. 
Colloidal  suspensions,  156. 
Compensation    method    of    determining 


electromotive  force,  161. 
Concentration  cells,  184. 
Concentration  double-cells,  211. 
Concepts  of  electrical  science,  1. 


Conductance,  at  high  temperatures,  132. 
Conductance,  calculation  from  migration 

velocity,  91. 

Conductance,  determination,  98. 
Conductance  of  electrolytes,  85. 
Conductance  of  solid  and  fused  salts,  153. 
Conductance  of  water,  128. 
Conductance,  specific  and  equivalent,  86. 
Conductance,  table,  88. 
Conductance,  technical  importance,  155. 
Conductors,  first  and  second  class,  33. 
Constitution  of  ions,  45. 
Corresponding,   or  isohydric,    solutions, 

136. 

Coulomb,  definition,  10. 
Course  of  electro-chemical  reactions,  281. 
Current  density,  165. 
Current  production,  process  of,  263. 


Daniell  cell,  50. 

Decomposition  of  water,  primary  and 
secondary,  288. 

Decomposition  point,  297. 

Decomposition  voltage  and  solubility,.  318. 

Decomposition  voltages,  importance,  309. 

Degree  of  dissociation,  calculation,  58. 

Depolarization,  definition,  312. 

Dielectric  constant,  definition  and  meas- 
urement, 142. 

Dielectric  constant,  relation  to  dissociat- 
ing power,  147. 

Displacement  of  equilibrium  by  temper- 
ature changes,  132. 

Dissociating  power,  or  capacity,  of  liquids, 
142. 

Dissociation  constant,  calculation  from 
conductance  values,  105. 

Dissociation  constant,  definition,  97. 

Dissociation  constant,  relation  to  chemi- 
cal constitution,  111. 

Dissociation  heat,  134. 

Dissociation  of  dibasic  acids,  first  and 
second  hydrogen,  113. 

Dissociation  of  water,  128. 


Dissociation  pressure  or  tension,  272. 
Dissociation  theory  of  Arrhenius,  52. 
Distant-action,  chemical,  261. 
Double-natured  elements,  284. 
336 


SUBJECT  INDEX 


337 


Double-natured  ions,  80. 
Drop-electrode,  239. 

Electric  furnace,  18. 

Electrical  and  chemical  energy,  relation, 
165. 

Electrical  conductance  in  chemical  analy- 
sis, 136. 

Electrical  conductance  of  electrolytes,  de- 
termination, 98. 

Electrical  discharge,  dark  or  silent,  23. 

Electrical  double-layer,  applied  to  col- 
loids, 242. 

Electrical  double-layer,  applied  to  Lipp- 
mann  electrometer,  235. 

Electricity,  material  conception  of,  60. 

Electro-chemical  change,  Faraday's  law, 
42. 

Electro-chemical  constant,  43. 

Electro-chemical  nomenclature,  44. 

Electro-chemical  theory  of  Berzelius,  40. 

Electro-chemical  reaction,  theory,  281. 

Electrode  potentials,  importance,  267. 

Electrolysis  and  polarization,  286. 

Electrolysis,  conceptions  of,  44. 

Electrolysis  with  an  alternating  current, 
316. 

Electrolysis  without  electrodes,  317. 

Electrolytic  dissociation,  theory,  284. 

Electrolytic  frictional  resistance,  123. 

Electrolytic  gas  constant  f—\ ,  182. 


Electrolytic  potentials  (EP),  247. 

Electrolytic  preparations  based  on  decom- 
position voltages,  309. 

Electrolytic  separation  based  on  decompo- 
sition voltages,  309. 

Electrolytic  solution  pressure,  175. 

Electrolytic  versus  gaseous  dissociation, 
59. 

Electrometer,  use  of,  as  an  indicator  in 
titration,  216. 

Electrometric  measurements,  28. 

Electromotive  force  and  chemical  equi- 
librium, 267. 

Electromotive  force  at  reversible  elec- 
trodes, calculation,  181. 

Electromotive  force,  conception  of,  7. 

Electromotive  force,  determination,  161. 

Electromotive  series,  law  of,  34,  221,  230. 

Electromotive  valence,  255. 

Electro-stenolysis,  159. 

Elements,  double-natured,  284. 

Empirical  rules  relating  to  conductance 
of  electrolytes,  125. 

Endosmose,  electrical,  157. 

Energetics,  first  law,  165. 

Energetics,  second  law,  166. 

Energy  forms,  1. 


Energy  transformations,  galvanic,  259. 
Equilibrium  at  an  electrode,  conditions, 

261. 

Equivalent  conductance  at  18%  table,  88. 
Equivalent  conductance,  definition,  85. 

Farad,  definition,  25. 
Faraday's  law,  42. 
Ferri-ferro  electrode,  263. 
First  law  of  energetics,  165. 
Fused  salts,  conductance  of,  153. 

Gas  constant,  B,  57. 

Gas  electrodes,  preparation  of,  194. 

Gaseous  and  electrolytic  dissociation,  dif- 
ferences between,  59. 

Gravity,  influence  on  electromotive  phe- 
nomena, 193. 

Grotthus  theory  of  electrolysis,  44. 

Heat  of  dissociation,  133. 
Heat  equivalent,  electrical,  17. 
Heat  equivalent,  mechanical,  17. 
Helmholtz   equation,  application  to  con- 
centration cells,  224. 
Helmholtz  heat  effect,  249. 
Helmholtz  standard  cell,  163. 
Holding-power  of  ions,  292,  308. 
Hydration  of  ions,  determination ,  78. 
Hydrogen  electrode,  reversibility,  194. 
Hydrogen-oxygen  cell,  288. 
Hydrogen,  spontaneous  evolution,  263. 

Indicator,  electrometer  in  titration,  216. 
Internal  friction,  relation  to  conductance, 

151. 
lonization,  according  to  the  materialistic 

theory  of  electricity,  60. 
lonization,  regularity,  62. 
Ions,  absolute  migration  velocity,  119. 
Ions,  constitution,  75. 
Ions,  double-natured,  80. 
Ions,  hyd ration,  78. 
Ions,  relative  migration  velocity,  71. 
Ions,  velocity  of  formation,  275. 
Irreversible  and  reversible  cells,  164. 
Isohydric  solutions,  136. 

Joule,  definition,  2. 
Joule's  law,  18. 

Kohlrausch's  law,  89,  91. 
Kohlrausch  method  of  determining  elec- 
trical conductance,  98. 

Law  of  Dilution,  Ostwald's,  124. 

Law      of      Faraday      (electro-chemical 

change),  42. 
Law  of  Joule,  18. 
Law  of  Kohlrausch,  91. 


338 


SUBJECT   INDEX 


Law  of  mass-action,  95. 

Law  of  Ohm,  8. 

Law  of  pressure-volume  product  (Boyle- 
Mario  tte),  53. 

Liquid  cells,  217. 

Luckow's  process,  preparation  of  chem- 
ical compounds,  276. 

Mass-action  law,  95. 
Mercury  process,  caustic  soda,  82. 
Metallic  mixtures  as  electrodes,  185. 
Migration  of  ions,  62. 
Migration  velocity  of  ions,  71. 
Migration  velocity  of  ions,  absolute,  119. 
Migration  velocity  of  ions,  table,  121. 
Mixed  solutions,  conductance,  136. 
Mobility,  or  migration  velocity,  of  ions,  71. 
Molecular  weight  determination,  electri- 
cal method,  184. 

Nitrogen,  fixation  from  the  atmosphere, 

22. 

Non-polarizable  electrodes,  165. 
Normal  or  standard  cells,  163. 

Ohm,  definition,  8. 

Ohm's  law,  8. 

Osmotic  pressure,  52. 

Ostwald's  dilution  law,  limited  applica- 
tion, 124. 

Over-voltage,  298. 

Oxidation  and  reduction  cells,  250. 

Oxidation,  electrolytic,  255. 

Oxidizing  agents,  electromotive  activity, 
312. 

Oxygen,  spontaneous  evolution,  263. 

Passivity,  275. 

Peltier  heat  effect,  249. 

Physical  constitution  of  metals,  influence 

on  electrolytic  phenomena,  193. 
Polarizable  electrodes,  165. 
Polarization,  measurement,  286. 
Potential-difference,    formation    at    the 

electrode,  263. 
Pressure,  influence  on  conductance,  135. 

Reactivity  of  electrolytes,  141. 
Reducing  agents,  electromotive  activity, 

312. 

Reduction  and  oxidation  cells,  250. 
Reduction,  electrolytic,  255. 
Relative  migration  velocity,  71. 
Relative  strengths  of  acids  and  bases,  95. 
Residual  current,  297. 
Resistance,  electrical,  7. 
Resistance,  electrolytic  frictional,  123. 
Reversible  and  irreversible  cells,  164. 


Second  law  of  energetics,  166. 

Siemens  units,  85. 

Single  potential-differences,  234. 

Solubility,  calculation  from  electromotive 
force,  206. 

Solubility,  determination  by  means  of 
electrical  conductance,  140. 

Solubility,  relation  to  decomposition  volt- 
age, 318. 

Solution  pressure,  electrolytic,  175. 

Solutions  of  metals,  behavior  as  elec- 
trodes, 186. 

Solvents  other  than  water,  electrical  con- 
ductance, 142. 

Solvents  other  than  water,  electromotive 
force,  249. 

Specific  conductance,  or  conductivity, 
definition,  85. 

Standard,  or  normal,  cells,  163. 

Strength  of  acids  and  bases,  95. 

Storage  cells  or  accumulators,  321. 

Superposition  principle  of  Nernst,  220. 

Supersaturated  solutions,  conductance 
of,  129. 

Surface  tension  of  mercury,  relation  to 
polarization,  234. 

Suspended  particles,  migration  of,  157. 

Temperature  changes,  effect  on  electrical 
conductance,  130. 

Thezmo-electric  cells,  228. 

Transference  numbers,  definition,  70. 

Transference  numbers,  determination,  72. 

Transference  numbers,  table,  84. 

Transference  phenomena,  technical  im- 
portance, 81. 

Transformation  of  an  alternating  into  a 
direct  current,  155. 

Transformation  pressure,  251. 

Transition  points,  determination  by 
means  of  E.  M.  F.  measurements,  271. 

Unipolar  conduction,  154. 

Valence,  electromotive,  255. 

Velocity  of  ionization,  275. 

Velocity  of   migration,   individual  ions, 

116. 

Volt,  definition,  7. 
Voltaic  pile,  33. 

Water,  electrical  conductance  and  degree 
of  dissociation,  128. 

Water,  primary  and  secondary  decom- 
position, 302,  308. 

Watt,  definition,  18. 

Weston,  or  cadmium,  standard  cell,  163. 


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PRINCIPLES  OF  INORGANIC  CHEMISTRY 

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THE  ELEMENTS  OF  PHYSICAL  CHEMISTRY 

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THE  THEORY  OF  ELECTROLYTIC  DISSOCIATION 
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ELEMENTS  OF  INORGANIC  CHEMISTRY 

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THE  PRACTICAL  METHODS  OF  ORGANIC 
CHEMISTRY 

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illustrations 

Translated  by  William  R.  Shober,  Ph.D.,  Instructor  in  Organic  Chemistry  in 
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